scholarly journals Free fermions at the edge of interacting systems

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Jean-Marie Stéphan
Keyword(s):  
Quantum Systems ◽  
Theoretical Explanation ◽  
Strong Interactions ◽  
Analytical Prediction ◽  
One Dimensional ◽  
Quantum Quenches ◽  
Edge Distribution ◽  
Interacting Systems ◽  
Universality Classes ◽  
Spatially Varying

We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at the edge, which simply explains the survival of Tracy-Widom scaling in general. For integrable systems, it is possible to push this argument further, and determine exactly the remaining length scale which controls the variance of the edge distribution. This analytical prediction is checked numerically, with excellent agreement. We also study numerically the edge scaling at fronts generated by quantum quenches, which provide new universality classes awaiting theoretical explanation.

scholarly journals Entanglement dynamics after quantum quenches in generic integrable systems

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Vincenzo Alba ◽  
Pasquale Calabrese
Keyword(s):  
Entanglement Entropy ◽  
Maximum Velocity ◽  
Quantum Systems ◽  
Analytic Description ◽  
One Dimensional ◽  
Quantum Quenches ◽  
Interacting Systems ◽  
Crucial Information ◽  
Quasiparticle Picture ◽  
Dependent State

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

scholarly journals Random matrix approaches to open quantum systems

2018 ◽  
Author(s):  
Henning Schomerus
Keyword(s):  
Random Matrix ◽  
Matrix Theory ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Mathematical Work ◽  
Mathematical Structures ◽  
Open Quantum ◽  
Interacting Systems ◽  
Universality Classes ◽  
Insight Into

Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. This chapter reviews the physical origins and mathematical structures of the underlying models, and collects key predictions which give insight into the typical system behaviour. In particular, the aim is to give an idea how the different features are interlinked. The chapter mainly focuses on elastic scattering but also includes a short detour to interacting systems, which are motivated by the overarching question of ergodicity. The first sections introduce general notions from random matrix theory, such as the 10 universality classes and ensembles of Hermitian, unitary, positive-definite, and non-Hermitian matrices. The following sections then review microscopic scattering models that form the basis for statistical descriptions, and consider signatures of random scattering in decay, dynamics, and transport. The last section touches on Anderson localization and localization in interacting systems.

Dynamics of One-Dimensional Quantum Systems

2009 ◽  
Author(s):  
Yoshio Kuramoto ◽  
Yusuke Kato
Keyword(s):  
Quantum Systems ◽  
One Dimensional

scholarly journals Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction

2020 ◽  
Vol 102 (5) ◽  
Author(s):  
Jean-Baptiste Fouvry ◽  
Pierre-Henri Chavanis ◽  
Christophe Pichon
Keyword(s):  
Kinetic Theory ◽  
Long Range ◽  
One Dimensional ◽  
Interacting Systems ◽  
Arbitrary Potential

scholarly journals One-dimensional many-body entangled open quantum systems with tensor network methods

2018 ◽  
Vol 4 (1) ◽  
pp. 013001 ◽  
Author(s):  
Daniel Jaschke ◽  
Simone Montangero ◽  
Lincoln D Carr
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Many Body ◽  
One Dimensional ◽  
Open Quantum ◽  
Tensor Network ◽  
Network Methods

scholarly journals Bad metallic transport in a cold atom Fermi-Hubbard system

Science ◽  
2018 ◽  
Vol 363 (6425) ◽  
pp. 379-382 ◽  
Author(s):  
Peter T. Brown ◽  
Debayan Mitra ◽  
Elmer Guardado-Sanchez ◽  
Reza Nourafkan ◽  
Alexis Reymbaut ◽  
...  
Keyword(s):  
Diffusion Constant ◽  
Cold Atom ◽  
Quantum Systems ◽  
Strong Interactions ◽  
Einstein Relation ◽  
Linear Temperature Dependence ◽  
Many Body ◽  
Linear Temperature ◽  
Density Modulation ◽  
Shed Light

Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold lithium-6 in a two-dimensional optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity by using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we developed in this study may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.

scholarly journals Hybrid Semiclassical Theory of Quantum Quenches in One-Dimensional Systems

2017 ◽  
Vol 119 (10) ◽  
Author(s):  
Cătălin Paşcu Moca ◽  
Márton Kormos ◽  
Gergely Zaránd
Keyword(s):  
Semiclassical Theory ◽  
One Dimensional ◽  
Quantum Quenches

scholarly journals Probing the edge between integrability and quantum chaos in interacting few-atom systems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 486
Author(s):  
Thomás Fogarty ◽  
Miguel Ángel García-March ◽  
Lea F. Santos ◽  
Nathan L. Harshman
Keyword(s):  
Quantum Chaos ◽  
Cold Atoms ◽  
Quantum Systems ◽  
Particle Interactions ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
The Core ◽  
Emergence Of Chaos ◽  
Number Of Particles

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

scholarly journals Transport in one-dimensional integrable quantum systems

2020 ◽  
Author(s):  
Jesko Sirker
Keyword(s):  
Transport Properties ◽  
Spin Chain ◽  
Linear Response ◽  
Summer School ◽  
Condensed Matter ◽  
Quantum Systems ◽  
Integrable Models ◽  
One Dimensional ◽  
Integrable Quantum ◽  
Linear Response Regime

These notes are based on a series of three lectures given at the Les Houches summer school on ’Integrability in Atomic and Condensed Matter Physics’ in August 2018. They provide an introduction into the unusual transport properties of integrable models in the linear response regime focussing, in particular, on the spin-1/21/2 XXZ spin chain.

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