Publications

Order by: publication date number of citations

• Topological chiral modes in random scattering networks

  Pierre A. L. Delplace

  SciPost Phys. 8, 081 (2020) · published 29 May 2020 | Toggle abstract · pdf

  Using elementary graph theory, we show the existence of interface chiral modes in random oriented scattering networks and discuss their topological nature. For particular regular networks (e.g. L-lattice, Kagome and triangular networks), an explicit mapping with time-periodically driven (Floquet) tight-binding models is found. In that case, the interface chiral modes are identified as the celebrated anomalous edge states of Floquet topological insulators and their existence is enforced by a symmetry imposed by the associated network. This work thus generalizes these anomalous chiral states beyond Floquet systems, to a class of discrete-time dynamical systems where a periodic driving in time is not required.

  16 citations

• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems

  Da-Chuan Lu, Zhengdi Sun, Yi-Zhuang You

  SciPost Phys. 17, 136 (2024) · published 15 November 2024 | Toggle abstract · pdf

  In this paper, we study the twisted gauging on the (1+1)d lattice and construct various non-local mappings on the lattice operators. To be specific, we define the twisted Gauss law operator and implement the twisted gauging of the finite group on the lattice motivated by the orbifolding procedure in the conformal field theory, which involves the data of non-trivial element in the second cohomology group of the gauge group. We show the twisted gauging is equivalent to the two-step procedure of first applying the SPT entangler and then untwisted gauging. We use the twisted gauging to construct the triality (order 3) and $p$-ality (order $p$) mapping on the $\mathbb{Z}_p× \mathbb{Z}_p$ symmetric Hamiltonians, where $p$ is a prime. Such novel non-local mappings generalize Kramers-Wannier duality and they preserve the locality of symmetric operators but map charged operators to non-local ones. We further construct quantum process to realize these non-local mappings and analyze the induced mappings on the phase diagrams. For theories that are invariant under these non-local mappings, they admit the corresponding non-invertible symmetries. The non-invertible symmetry will constrain the theory at the multicritical point between the gapped phases. We further give the condition when the non-invertible symmetry can have symmetric gapped phase with a unique ground state.

  16 citations

• Measurement induced transitions in non-Markovian free fermion ladders

  Mikheil Tsitsishvili, Dario Poletti, Marcello Dalmonte, Giuliano Chiriacò

  SciPost Phys. Core 7, 011 (2024) · published 12 March 2024 | Toggle abstract · pdf

  Recently there has been an intense effort to understand measurement induced transitions, but we still lack a good understanding of non-Markovian effects on these phenomena. To that end, we consider two coupled chains of free fermions, one acting as the system of interest, and one as a bath. The bath chain is subject to Markovian measurements, resulting in an effective non-Markovian dissipative dynamics acting on the system chain which is still amenable to numerical studies in terms of quantum trajectories. Within this setting, we study the entanglement within the system chain, and use it to characterize the phase diagram depending on the ladder hopping parameters and on the measurement probability. For the case of pure state evolution, the system is in an area law phase when the internal hopping of the bath chain is small, while a non-area law phase appears when the dynamics of the bath is fast. The non-area law exhibits a logarithmic scaling of the entropy compatible with a conformal phase, but also displays linear corrections for the finite system sizes we can study. For the case of mixed state evolution, we instead observe regions with both area, and non-area scaling of the entanglement negativity. We quantify the non-Markovianity of the system chain dynamics and find that for the regimes of parameters we study, a stronger non-Markovianity is associated to a larger entanglement within the system.

  16 citations

• Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories

  Patrick Emonts, Erez Zohar

  SciPost Phys. Lect. Notes 12 (2020) · published 17 January 2020 | Toggle abstract · pdf

  In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced, by looking at the Gauss law from two different points of view: for the gauge field it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in terms of unitarily gauging a pure-matter theory and eliminating the matter from a gauge theory, and relate that to the construction of PEPS (Projected Entangled Pair States) for lattice gauge theories.

  16 citations

• Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

  João C. Getelina, Niladri Gomes, Thomas Iadecola, Peter P. Orth, Yong-Xin Yao

  SciPost Phys. 15, 102 (2023) · published 19 September 2023 | Toggle abstract · pdf

  Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

  15 citations

• Ownerless island and partial entanglement entropy in island phases

  Debarshi Basu, Jiong Lin, Yizhou Lu, Qiang Wen

  SciPost Phys. 15, 227 (2023) · published 6 December 2023 | Toggle abstract · pdf

  In the context of partial entanglement entropy (PEE), we study the entanglement structure of the island phases realized in several 2-dimensional holographic set-ups. From a pure quantum information perspective, the entanglement islands emerge from the self-encoding property of the system, which gives us new insights on the construction of the PEE and the physical interpretation of two-point functions of twist operators in island phases. With the contributions from the entanglement islands properly taken into account, we give a generalized prescription to construct PEE and balanced partial entanglement entropy (BPE). Here the ownerless island region, which lies inside the island $\text{Is}(AB)$ of $A\cup B$ but outside $\text{Is}(A)\cup \text{Is}(B)$, plays a crucial role. Remarkably, we find that under different assignments for the ownerless island, we get different BPEs, which exactly correspond to different saddles of the entanglement wedge cross-section (EWCS) in the entanglement wedge of $A\cup B$. The assignments can be settled by choosing the one that minimizes the BPE. Furthermore, under this assignment we study the PEE and give a geometric picture for the PEE in holography, which is consistent with the geometric picture in the no-island phases.

  15 citations

• Quantum Gross-Pitaevskii Equation

  Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

  SciPost Phys. 3, 006 (2017) · published 28 July 2017 | Toggle abstract · pdf

  We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

  15 citations

• Completeness of the Bethe states for the rational, spin-1/2 Richardson-Gaudin system

  Jon Links

  SciPost Phys. 3, 007 (2017) · published 28 July 2017 | Toggle abstract · pdf

  Establishing the completeness of a Bethe Ansatz solution for an exactly solved model is a perennial challenge, which is typically approached on a case by case basis. For the rational, spin-1/2 Richardson--Gaudin system it will be argued that, for generic values of the system's coupling parameters, the Bethe states are complete. This method does not depend on knowledge of the distribution of Bethe roots, such as a string hypothesis, and is generalisable to a wider class of systems.

  15 citations

• Real-time evolution in the Hubbard model with infinite repulsion

  Elena Tartaglia, Pasquale Calabrese, Bruno Bertini

  SciPost Phys. 12, 028 (2022) · published 18 January 2022 | Toggle abstract · pdf

  We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless fermions, i.e. the tight binding model. The relevant local observables, however, do not transform well under this mapping and take very complicated expressions in terms of the spinless fermions. Here we show that for two classes of interesting observables the quench dynamics from product states in the occupation basis can be determined exactly in terms of correlations in the tight-binding model. In particular, we show that the time evolution of any function of the total density of particles is mapped directly into that of the same function of the density of spinless fermions in the tight-binding model. Moreover, we express the two-point functions of the spin-full fermions at any time after the quench in terms of correlations of the tight binding model. This sum is generically very complicated but we show that it leads to simple explicit expressions for the time evolution of the densities of the two separate species and the correlations between a point at the boundary and one in the bulk when evolving from the so called generalised nested Néel states.

  15 citations

• Strongly-interacting bosons at 2D-1D dimensional crossover

  Hepeng Yao, Lorenzo Pizzino, Thierry Giamarchi

  SciPost Phys. 15, 050 (2023) · published 7 August 2023 | Toggle abstract · pdf

  We study a two dimensional (2D) system of interacting quantum bosons, subjected to a continuous periodic potential in one direction. The correlation of such system exhibits a dimensional crossover between a canonical 2D behavior with Berezinski-Kosterlitz-Thouless (BKT) properties and a one-dimensional (1D) behavior when the potential is large and splits the system in essentially independent tubes. The latter is in the universality class of Tomonaga-Luttinger liquids (TLL). Using a continuous quantum Monte Carlo method, we investigate this dimensional crossover by computing longitudinal and transverse superfluid fraction as well as the superfluid correlation as a function of temperature, interactions and potential. Especially, we find the correlation function evolves from BKT to TLL type, with special intermediate behaviors appearing at the dimensional crossover. We discuss how the consequences of the dimensional crossover can be investigated in cold atomic gases experiments.

  15 citations