Publications

Order by: publication date number of citations

• Front dynamics in the XY chain after local excitations

  Viktor Eisler, Florian Maislinger

  SciPost Phys. 8, 037 (2020) · published 6 March 2020 | Toggle abstract · pdf

  We study the time evolution of magnetization and entanglement for initial states with local excitations, created upon the ferromagnetic ground state of the XY chain. For excitations corresponding to a single or two well separated domain walls, the magnetization profile has a simple hydrodynamic limit, which has a standard interpretation in terms of quasiparticles. In contrast, for a spin-flip we obtain an interference term, which has to do with the nonlocality of the excitation in the fermionic basis. Surprisingly, for the single domain wall the hydrodynamic limit of the entropy and magnetization profiles are found to be directly related. Furthermore, the entropy profile is additive for the double domain wall, whereas in case of the spin-flip excitation one has a nontrivial behaviour.

  18 citations

• Rigorous bounds on dynamical response functions and time-translation symmetry breaking

  Marko Medenjak, Tomaz Prosen, Lenart Zadnik

  SciPost Phys. 9, 003 (2020) · published 7 July 2020 | Toggle abstract · pdf

  Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e. extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

  18 citations

• Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

  Thomas Köhler, Jan Stolpp, Sebastian Paeckel

  SciPost Phys. 10, 058 (2021) · published 9 March 2021 | Toggle abstract · pdf

  Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial $U(1)$ symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrix\hyp product\hyp state representation and the single\hyp site reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to $L=501$ while accounting for $N_{\rm ph}=63$ phonons per site with high precision in the CDW phase.

  18 citations

• Many-body localization of spinless fermions with attractive interactions in one dimension

  Sheng-Hsuan Lin, Björn Sbierski, Florian Dorfner, Christoph Karrasch, Fabian Heidrich-Meisner

  SciPost Phys. 4, 002 (2018) · published 18 January 2018 | Toggle abstract · pdf

  We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of one-particle density matrices is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization scheme to study the finite-size dependence of the conductance, which resolves the existence of the Luttinger liquid as well and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

  18 citations

• DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

  P. Myles Eugenio, Ceren B. Dağ

  SciPost Phys. Core 3, 015 (2020) · published 9 December 2020 | Toggle abstract · pdf

  Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern$=\pm1$), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL's with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL's with the same magnetic field. In the first scenario -- which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene -- the opposite Chern LLL's are Kramer pairs, and thus there exists time-reversal symmetry ($\mathbb{Z}_2$). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry -- a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern $|++\cdots+>$ or all negative $|--\cdots->$. If instead, interactions are taken between electrons of like-Chern number, the ground state is an $SU(2)$ ferromagnet, with total spin pointing along an arbitrary direction, as with the $\nu=1$ spin-$\frac{1}{2}$ quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

  18 citations

• Comments on black hole interiors and modular inclusions

  Ro Jefferson

  SciPost Phys. 6, 042 (2019) · published 5 April 2019 | Toggle abstract · pdf

  We show how the traversable wormhole induced by a double-trace deformation of the thermofield double state can be understood as a modular inclusion of the algebras of exterior operators. The effect of this deformation is the creation of a new region of spacetime deep in the bulk, corresponding to a non-trivial center between the left and right algebras. This set-up provides a precise framework for investigating how black hole interiors are encoded in the CFT. In particular, we use modular theory to demonstrate that state dependence is an inevitable feature of any attempt to represent operators behind the horizon. Building on this geometrical structure, we propose that modular inclusions may provide a more precise means of investigating the nascent relationship between entanglement and geometry in the context of the emergent spacetime paradigm.

  17 citations

• Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

  Sophie S. Shamailov, Joachim Brand

  SciPost Phys. 4, 018 (2018) · published 31 March 2018 | Toggle abstract · pdf

  Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.

  17 citations

• Phase-space methods for simulating the dissipative many-body dynamics of collective spin systems

  Julian Huber, Peter Kirton, Peter Rabl

  SciPost Phys. 10, 045 (2021) · published 22 February 2021 | Toggle abstract · pdf

  We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.

  16 citations

• Abelian and non-abelian symmetries in infinite projected entangled pair states

  Claudius Hubig

  SciPost Phys. 5, 047 (2018) · published 9 November 2018 | Toggle abstract · pdf

  We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions $D = 10$ in the square lattice Heisenberg model at computational effort comparable to calculations at $D = 6$ without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.

  16 citations

• Floquet conformal field theories with generally deformed Hamiltonians

  Ruihua Fan, Yingfei Gu, Ashvin Vishwanath, Xueda Wen

  SciPost Phys. 10, 049 (2021) · published 25 February 2021 | Toggle abstract · pdf

  In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.

  16 citations