Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases
Jérôme Dubail, Jean-Marie Stéphan, Jacopo Viti, Pasquale Calabrese
SciPost Phys. 2, 002 (2017) · published 13 February 2017
- doi: 10.21468/SciPostPhys.2.1.002
- Submissions/Reports
Abstract
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system's inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means.
TY - JOUR
PB - SciPost Foundation
DO - 10.21468/SciPostPhys.2.1.002
TI - Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases
PY - 2017/02/13
UR - https://scipost.org/SciPostPhys.2.1.002
JF - SciPost Physics
JA - SciPost Phys.
VL - 2
IS - 1
SP - 002
A1 - Dubail, Jerome
AU - Stéphan, Jean-Marie
AU - Viti, Jacopo
AU - Calabrese, Pasquale
AB - Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system's inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means.
ER -
@Article{10.21468/SciPostPhys.2.1.002,
title={{Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases}},
author={Jérôme Dubail and Jean-Marie Stéphan and Jacopo Viti and Pasquale Calabrese},
journal={SciPost Phys.},
volume={2},
pages={002},
year={2017},
publisher={SciPost},
doi={10.21468/SciPostPhys.2.1.002},
url={https://scipost.org/10.21468/SciPostPhys.2.1.002},
}
Cited by 160
-
Calabrese, Entanglement spreading in non-equilibrium integrable systems
SciPost Phys. Lect. Notes, 20 (2020) [Crossref] -
Murciano et al., More on symmetry resolved operator entanglement
J. Phys. A: Math. Theor. 57, 145002 (2024) [Crossref] -
Rodríguez-Laguna et al., More on the rainbow chain: entanglement, space-time geometry and thermal states
J. Phys. A: Math. Theor. 50, 164001 (2017) [Crossref] -
Scopa et al., Scaling of fronts and entanglement spreading during a domain wall melting
Eur. Phys. J. Spec. Top. 232, 1763 (2023) [Crossref] -
Cao et al., Entanglement in a fermion chain under continuous monitoring
SciPost Phys. 7, 024 (2019) [Crossref] -
Bertini et al., Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics
Phys. Rev. B 100, 035108 (2019) [Crossref] -
MacCormack et al., Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model
J. Phys. A: Math. Theor. 52, 505401 (2019) [Crossref] -
Parez et al., Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
J. Stat. Mech. 2021, 093102 (2021) [Crossref] -
Mestyán et al., Rényi entropies of generic thermodynamic macrostates in integrable systems
J. Stat. Mech. 2018, 083104 (2018) [Crossref] -
Lapierre et al., Geometric approach to inhomogeneous Floquet systems
Phys. Rev. B 103, 224303 (2021) [Crossref] -
Choo et al., Thermal and dissipative effects on the heating transition in a driven critical system
SciPost Phys. 13, 104 (2022) [Crossref] -
Finkel et al., Inhomogeneous XX spin chains and quasi-exactly solvable models
J. Stat. Mech. 2020, 093105 (2020) [Crossref] -
Goto et al., Spatial deformation of many-body quantum chaotic systems and quantum information scrambling
Phys. Rev. B 109, 054301 (2024) [Crossref] -
Di Ubaldo et al., Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics
J. High Energ. Phys. 2023, 122 (2023) [Crossref] -
Rottoli et al., Entanglement Hamiltonian during a domain wall melting in the free Fermi chain
J. Stat. Mech. 2022, 063103 (2022) [Crossref] -
De Luca et al., Nonequilibrium spin transport in integrable spin chains: Persistent currents and emergence of magnetic domains
Phys. Rev. B 96, 020403 (2017) [Crossref] -
Bertini et al., Entanglement evolution and generalised hydrodynamics: noninteracting systems
J. Phys. A: Math. Theor. 51, 39LT01 (2018) [Crossref] -
Scopa et al., One-particle density matrix and momentum distribution of the out-of-equilibrium one-dimensional Tonks-Girardeau gas: Analytical results at large
N
Phys. Rev. A 108, 013324 (2023) [Crossref] -
Alba et al., Unusual area-law violation in random inhomogeneous systems
J. Stat. Mech. 2019, 023105 (2019) [Crossref] -
Misguich et al., Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
SciPost Phys. 7, 025 (2019) [Crossref] -
Ruggiero et al., Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
SciPost Phys. 11, 055 (2021) [Crossref] -
Bastianello et al., Entanglement spreading and quasiparticle picture beyond the pair structure
SciPost Phys. 8, 045 (2020) [Crossref] -
Moosavi, Exact Dirac–Bogoliubov–de Gennes Dynamics for Inhomogeneous Quantum Liquids
Phys. Rev. Lett. 131, 100401 (2023) [Crossref] -
Caputa et al., Geometry and complexity of path integrals in inhomogeneous CFTs
J. High Energ. Phys. 2021, 27 (2021) [Crossref] -
Smith et al., Full counting statistics for interacting trapped fermions
SciPost Phys. 11, 110 (2021) [Crossref] -
Bastianello et al., Exact Local Correlations and Full Counting Statistics for Arbitrary States of the One-Dimensional Interacting Bose Gas
Phys. Rev. Lett. 120, 190601 (2018) [Crossref] -
Ares et al., Sublogarithmic behaviour of the entanglement entropy in fermionic chains
J. Stat. Mech. 2019, 093105 (2019) [Crossref] -
Zhang et al., Subsystem trace distance in low-lying states of (1 + 1)-dimensional conformal field theories
J. High Energ. Phys. 2019, 181 (2019) [Crossref] -
Kulkarni et al., Quantum quench and thermalization of one-dimensional Fermi gas via phase-space hydrodynamics
Phys. Rev. A 98, 043610 (2018) [Crossref] -
van Nieuwkerk et al., On the low-energy description for tunnel-coupled one-dimensional Bose gases
SciPost Phys. 9, 025 (2020) [Crossref] -
Coppola et al., Wigner dynamics for quantum gases under inhomogeneous gain and loss processes with dephasing
Phys. Rev. A 107, 052213 (2023) [Crossref] -
Modak et al., Entanglement revivals as a probe of scrambling in finite quantum systems
J. Stat. Mech. 2020, 083110 (2020) [Crossref] -
Eisler, Entanglement Hamiltonian of a nonrelativistic Fermi gas
Phys. Rev. B 109, L201113 (2024) [Crossref] -
Parez et al., Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
J. Stat. Mech. 2022, 053103 (2022) [Crossref] -
Fagotti, Global Quenches after Localized Perturbations
Phys. Rev. Lett. 128, 110602 (2022) [Crossref] -
Ruggiero et al., Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
SciPost Phys. 6, 051 (2019) [Crossref] -
Alba et al., Entanglement evolution and generalised hydrodynamics: interacting integrable systems
SciPost Phys. 7, 005 (2019) [Crossref] -
Moosavi, Inhomogeneous Conformal Field Theory Out of Equilibrium
Ann. Henri Poincaré 25, 1083 (2024) [Crossref] -
Unterberger, Global fluctuations for 1D log-gas dynamics. Covariance kernel and support
Electron. J. Probab. 24, (2019) [Crossref] -
Ares et al., Entanglement dynamics of a hard-core quantum gas during a Joule expansion
J. Phys. A: Math. Theor. 55, 375301 (2022) [Crossref] -
Tajik et al., Experimental observation of curved light-cones in a quantum field simulator
Proc. Natl. Acad. Sci. U.S.A. 120, e2301287120 (2023) [Crossref] -
Fagotti, Locally quasi-stationary states in noninteracting spin chains
SciPost Phys. 8, 048 (2020) [Crossref] -
Alba et al., Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit
Phys. Rev. B 105, 054303 (2022) [Crossref] -
Alba, Towards a generalized hydrodynamics description of Rényi entropies in integrable systems
Phys. Rev. B 99, 045150 (2019) [Crossref] -
Gruber et al., Time evolution of entanglement negativity across a defect
J. Phys. A: Math. Theor. 53, 205301 (2020) [Crossref] -
Smith et al., Counting statistics for noninteracting fermions in a
d
-dimensional potential
Phys. Rev. E 103, L030105 (2021) [Crossref] -
Gouraud et al., Quench dynamics of noninteracting fermions with a delta impurity
J. Phys. A: Math. Theor. 55, 395001 (2022) [Crossref] -
Bouchoule et al., Generalized hydrodynamics in the one-dimensional Bose gas: theory and experiments
J. Stat. Mech. 2022, 014003 (2022) [Crossref] -
Piroli et al., Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions
Phys. Rev. B 96, 115124 (2017) [Crossref] -
Mazza et al., Energy transport in an integrable parafermionic chain via generalized hydrodynamics
Phys. Rev. B 98, 075421 (2018) [Crossref] -
Monteiro et al., Tunneling times of an electron in one-dimensional symmetric and asymmetric harmonic double-well potentials
Eur. Phys. J. Plus 138, 718 (2023) [Crossref] -
Bastianello, Sine-Gordon model from coupled condensates: A generalized hydrodynamics viewpoint
Phys. Rev. B 109, 035118 (2024) [Crossref] -
Scopa et al., Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
J. Stat. Mech. 2022, 083104 (2022) [Crossref] -
Bernard et al., Entanglement of inhomogeneous free fermions on hyperplane lattices
Nuclear Physics B 984, 115975 115975 (2022) [Crossref] -
Brun et al., One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
SciPost Phys. 2, 012 (2017) [Crossref] -
Simón, Correlations vs connectivity in R-charge
J. High Energ. Phys. 2018, 48 (2018) [Crossref] -
Zhang et al., Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
Phys. Rev. A 97, 023605 (2018) [Crossref] -
Mussardo et al., ℏ→0
limit of the entanglement entropy
Phys. Rev. A 105, 032404 (2022) [Crossref] -
Bertini, Approximate light cone effects in a nonrelativistic quantum field theory after a local quench
Phys. Rev. B 95, 075153 (2017) [Crossref] -
Scopa et al., One-particle density matrix of a trapped Lieb–Liniger anyonic gas
J. Stat. Mech. 2020, 093103 (2020) [Crossref] -
Goto et al., Scrambling and recovery of quantum information in inhomogeneous quenches in two-dimensional conformal field theories
Phys. Rev. Research 6, 023001 (2024) [Crossref] -
Eisler et al., Front dynamics and entanglement in the XXZ chain with a gradient
Phys. Rev. B 96, 174301 (2017) [Crossref] -
Gullans et al., Entanglement Structure of Current-Driven Diffusive Fermion Systems
Phys. Rev. X 9, 021007 (2019) [Crossref] -
Wang et al., Eigenstate thermalization and its breakdown in quantum spin chains with inhomogeneous interactions
Phys. Rev. B 109, 045139 (2024) [Crossref] -
Biella et al., Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
Nat Commun 10, 4820 (2019) [Crossref] -
De Bruyne et al., Wigner function for noninteracting fermions in hard-wall potentials
Phys. Rev. A 104, 013314 (2021) [Crossref] -
Gamayun et al., On Landauer–Büttiker formalism from a quantum quench
J. Phys. A: Math. Theor. 56, 205203 (2023) [Crossref] -
Colcelli et al., Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas
Phys. Rev. A 98, 063633 (2018) [Crossref] -
Doyon et al., A note on generalized hydrodynamics: inhomogeneous fields and other concepts
SciPost Phys. 2, 014 (2017) [Crossref] -
Bertini et al., Finite-temperature transport in one-dimensional quantum lattice models
Rev. Mod. Phys. 93, 025003 (2021) [Crossref] -
Fan et al., Floquet conformal field theories with generally deformed Hamiltonians
SciPost Phys. 10, 049 (2021) [Crossref] -
Bonsignori et al., Entanglement Hamiltonian for inhomogeneous free fermions
J. Phys. A: Math. Theor. 57, 275001 (2024) [Crossref] -
Tonni et al., Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
J. Stat. Mech. 2018, 043105 (2018) [Crossref] -
Pomponio et al., Quasi-particle spectrum and entanglement generation after a quench in the quantum Potts spin chain
J. Stat. Mech. 2019, 013104 (2019) [Crossref] -
Alba et al., Entanglement and thermodynamics after a quantum quench in integrable systems
Proc. Natl. Acad. Sci. U.S.A. 114, 7947 (2017) [Crossref] -
Alba et al., Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects
J. Stat. Mech. 2021, 114004 (2021) [Crossref] -
Fagotti, Higher-order generalized hydrodynamics in one dimension: The noninteracting test
Phys. Rev. B 96, 220302 (2017) [Crossref] -
Bertini et al., Entanglement and diagonal entropies after a quench with no pair structure
J. Stat. Mech. 2018, 063104 (2018) [Crossref] -
Murciano et al., Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
J. Stat. Mech. 2019, 034001 (2019) [Crossref] -
Panfil et al., Linearized regime of the generalized hydrodynamics with diffusion
SciPost Phys. Core 1, 002 (2019) [Crossref] -
Di Giulio et al., On entanglement Hamiltonians of an interval in massless harmonic chains
J. Stat. Mech. 2020, 033102 (2020) [Crossref] -
Gouraud et al., Stationary time correlations for fermions after a quench in the presence of an impurity
EPL 142, 41001 (2023) [Crossref] -
Bernamonti et al., Boundary-induced transitions in Möbius quenches of holographic BCFT
J. High Energ. Phys. 2024, 184 (2024) [Crossref] -
Wen et al., Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to nonuniform conformal field theory
Phys. Rev. B 97, 184309 (2018) [Crossref] -
Fagotti et al., Nonequilibrium symmetry-protected topological order: Emergence of semilocal Gibbs ensembles
Phys. Rev. B 109, 115117 (2024) [Crossref] -
Dean et al., Nonequilibrium dynamics of noninteracting fermions in a trap
EPL 126, 20006 (2019) [Crossref] -
Collura et al., Quantum quench in a harmonically trapped one-dimensional Bose gas
Phys. Rev. A 97, 033609 (2018) [Crossref] -
Capizzi et al., A hydrodynamic approach to Stark localization
J. Stat. Mech. 2023, 073104 (2023) [Crossref] -
Alba et al., Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories
J. Phys. A: Math. Theor. 51, 024001 (2018) [Crossref] -
Bastianello et al., Nonequilibrium Steady State Generated by a Moving Defect: The Supersonic Threshold
Phys. Rev. Lett. 120, 060602 (2018) [Crossref] -
Eisler et al., Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals
J. Stat. Mech. 2022, 083101 (2022) [Crossref] -
Samos Sáenz de Buruaga et al., Entanglement in noncritical inhomogeneous quantum chains
Phys. Rev. B 104, 195147 (2021) [Crossref] -
Bastianello et al., Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions
Phys. Rev. Lett. 123, 130602 (2019) [Crossref] -
Collura et al., Domain wall melting in the spin-
12
XXZ spin chain: Emergent Luttinger liquid with a fractal quasiparticle charge
Phys. Rev. B 102, 180409 (2020) [Crossref] -
Eisler, Entanglement spreading after local and extended excitations in a free-fermion chain
J. Phys. A: Math. Theor. 54, 424002 (2021) [Crossref] -
Fremling et al., Dynamics and level statistics of interacting fermions in the lowest Landau level
New J. Phys. 20, 103036 (2018) [Crossref] -
Bocini et al., Non-probabilistic fermionic limit shapes
J. Stat. Mech. 2021, 013204 (2021) [Crossref] -
Oblak et al., Anisotropic Quantum Hall Droplets
Phys. Rev. X 14, 011030 (2024) [Crossref] -
Bastianello et al., Generalized hydrodynamics with dephasing noise
Phys. Rev. B 102, 161110 (2020) [Crossref] -
Doyon et al., Dynamics of hard rods with initial domain wall state
J. Stat. Mech. 2017, 073210 (2017) [Crossref] -
Mestyán et al., Exact solution for the quench dynamics of a nested integrable system
J. Stat. Mech. 2017, 083103 (2017) [Crossref] -
Ruggiero et al., Quantum Generalized Hydrodynamics
Phys. Rev. Lett. 124, 140603 (2020) [Crossref] -
Boumaza et al., Analytical results for the time-dependent current density distribution of expanding ultracold gases after a sudden change of the confining potential
J. Phys. A: Math. Theor. 50, 505003 (2017) [Crossref] -
Ruggiero et al., Electrostatic solution of massless quenches in Luttinger liquids
SciPost Phys. 13, 111 (2022) [Crossref] -
Collura et al., Dynamical manifestation of the Gibbs paradox after a quantum quench
Phys. Rev. A 98, 053610 (2018) [Crossref] -
Zhang et al., Information measures for local quantum phase transitions: Lattice bosons in a one-dimensional harmonic trap
Phys. Rev. A 100, 053611 (2019) [Crossref] -
Scopa et al., Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
J. Phys. A: Math. Theor. 54, 404002 (2021) [Crossref] -
Ramírez,
1955, 030007 (2018) [Crossref] -
Alba et al., Entanglement dynamics after quantum quenches in generic integrable systems
SciPost Phys. 4, 017 (2018) [Crossref] -
Bonsignori et al., Symmetry resolved entanglement in free fermionic systems
J. Phys. A: Math. Theor. 52, 475302 (2019) [Crossref] -
Nozaki et al., Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
Phys. Rev. D 109, 126014 (2024) [Crossref] -
Ramírez et al.,
239, 395 (2020) [Crossref] -
Gluza et al., Breaking of Huygens–Fresnel principle in inhomogeneous Tomonaga–Luttinger liquids
J. Phys. A: Math. Theor. 55, 054002 (2022) [Crossref] -
Finkel et al., Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions
J. High Energ. Phys. 2021, 184 (2021) [Crossref] -
Mestyán et al., Spin-charge separation effects in the low-temperature transport of one-dimensional Fermi gases
Phys. Rev. B 99, 014305 (2019) [Crossref] -
Ares et al., Complex behavior of the density in composite quantum systems
Phys. Rev. B 102, 165121 (2020) [Crossref] -
Gawędzki et al., Finite-Time Universality in Nonequilibrium CFT
J Stat Phys 172, 353 (2018) [Crossref] -
Ruggiero et al., Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy
J. Phys. A: Math. Theor. 55, 024003 (2022) [Crossref] -
Langmann et al., Diffusive Heat Waves in Random Conformal Field Theory
Phys. Rev. Lett. 122, 020201 (2019) [Crossref] -
Chepiga, Probing universal critical scaling with scan density matrix renormalization group
Phys. Rev. B 110, 144401 (2024) [Crossref] -
Le Doussal et al., Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions
SciPost Phys. 17, 038 (2024) [Crossref] -
Doyon, Exact large-scale correlations in integrable systems out of equilibrium
SciPost Phys. 5, 054 (2018) [Crossref] -
Stéphan, Free fermions at the edge of interacting systems
SciPost Phys. 6, 057 (2019) [Crossref] -
Capizzi et al., Domain wall melting across a defect
EPL 141, 31002 (2023) [Crossref] -
Dubail, Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d
J. Phys. A: Math. Theor. 50, 234001 (2017) [Crossref] -
De Nardis et al., Edge Singularities and Quasilong-Range Order in Nonequilibrium Steady States
Phys. Rev. Lett. 120, 217206 (2018) [Crossref] -
Møller et al., Euler-scale dynamical correlations in integrable systems with fluid motion
SciPost Phys. Core 3, 016 (2020) [Crossref] -
Wen et al., Entanglement Hamiltonian evolution during thermalization in conformal field theory
J. Stat. Mech. 2018, 113103 (2018) [Crossref] -
Scopa et al., Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
SciPost Phys. 12, 207 (2022) [Crossref] -
Granet et al., Inhomogeneous Gaussian free field inside the interacting arctic curve
J. Stat. Mech. 2019, 013102 (2019) [Crossref] -
Ageev et al., Infrared regularization and finite size dynamics of entanglement entropy in Schwarzschild black hole
Phys. Rev. D 108, 046005 (2023) [Crossref] -
Kudler-Flam et al., Bridging two quantum quench problems — local joining quantum quench and Möbius quench — and their holographic dual descriptions
J. High Energ. Phys. 2024, 213 (2024) [Crossref] -
Bertini et al., Universal Broadening of the Light Cone in Low-Temperature Transport
Phys. Rev. Lett. 120, 176801 (2018) [Crossref] -
Balducci et al., Interface dynamics in the two-dimensional quantum Ising model
Phys. Rev. B 107, 024306 (2023) [Crossref] -
Doyon et al., Soliton Gases and Generalized Hydrodynamics
Phys. Rev. Lett. 120, 045301 (2018) [Crossref] -
Brun et al., The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
SciPost Phys. 4, 037 (2018) [Crossref] -
Gamayun et al., Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains
SciPost Phys. 8, 036 (2020) [Crossref] -
Eisler et al., Front dynamics in the XY chain after local excitations
SciPost Phys. 8, 037 (2020) [Crossref] -
Bermond et al., Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches
SciPost Phys. 16, 084 (2024) [Crossref] -
Dalmonte et al., Entanglement Hamiltonians: From Field Theory to Lattice Models and Experiments
Annalen der Physik 534, 2200064 (2022) [Crossref] -
Barfknecht et al., Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
Phys. Rev. Research 3, 013112 (2021) [Crossref] -
Kosior et al., Nonlinear entanglement growth in inhomogeneous space-times
Phys. Rev. Research 2, 043036 (2020) [Crossref] -
Stéphan, Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
J. Stat. Mech. 2017, 103108 (2017) [Crossref] -
Bernard et al., Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
J. Phys. A: Math. Theor. 57, 015002 (2024) [Crossref] -
Estienne et al., Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
J. High Energ. Phys. 2024, 236 (2024) [Crossref] -
Estienne et al., Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
SciPost Phys. 12, 141 (2022) [Crossref] -
De Jonckheere et al., Entanglement entropy in inhomogeneous quenches in
AdS3/CFT2
Phys. Rev. D 98, 106006 (2018) [Crossref] -
Bastianello, Rényi entanglement entropies for the compactified massless boson with open boundary conditions
J. High Energ. Phys. 2019, 141 (2019) [Crossref] -
Doyon et al., A geometric viewpoint on generalized hydrodynamics
Nuclear Physics B 926, 570 (2018) [Crossref] -
De Nardis et al., Diffusion in generalized hydrodynamics and quasiparticle scattering
SciPost Phys. 6, 049 (2019) [Crossref] -
Coppola et al., Conditional no-jump dynamics of noninteracting quantum chains
Phys. Rev. B 110, 094315 (2024) [Crossref] -
Alba, Entanglement and quantum transport in integrable systems
Phys. Rev. B 97, 245135 (2018) [Crossref] -
Gruber et al., Magnetization and entanglement after a geometric quench in the XXZ chain
Phys. Rev. B 99, 174403 (2019) [Crossref] -
Bastianello et al., Entanglement entropies of inhomogeneous Luttinger liquids
J. Phys. A: Math. Theor. 53, 155001 (2020) [Crossref] -
Dubail et al., Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
SciPost Phys. 3, 019 (2017) [Crossref] -
De Nardis et al., Particle-hole pairs and density–density correlations in the Lieb–Liniger model
J. Stat. Mech. 2018, 033102 (2018) [Crossref] -
Parez, Symmetry-resolved Rényi fidelities and quantum phase transitions
Phys. Rev. B 106, 235101 (2022) [Crossref] -
Bonsignori et al., Boundary effects on symmetry resolved entanglement
J. Phys. A: Math. Theor. 54, 015005 (2021) [Crossref] -
Collura et al., Analytic solution of the domain-wall nonequilibrium stationary state
Phys. Rev. B 97, 081111 (2018) [Crossref] -
Bertini et al., Low-temperature transport in out-of-equilibrium XXZ chains
J. Stat. Mech. 2018, 033104 (2018) [Crossref]
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Jerome Dubail,
- 1 3 4 Jean-Marie Stéphan,
- 5 Jacopo Viti,
- 6 7 Pasquale Calabrese
- 1 Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS]
- 2 Université de Lorraine [Univ Lorraine]
- 3 Claude Bernard University Lyon 1 [UCBL]
- 4 Max Planck Digital Library [MPDL]
- 5 Instituto Internacional de Fisica / International Institute of Physics
- 6 Istituto Nazionale di Fisica Nucleare (presso la SISSA) / National Institute of Nuclear Physics (at SISSA) [INFN at SISSA]
- 7 INFN Sezione di Bologna / INFN Bologna [INFN Bologna]