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.

scholarly journals Interaction instability of localization in quasiperiodic systems

2018 ◽  
Vol 115 (18) ◽  
pp. 4595-4600 ◽  
Author(s):  
Marko Žnidarič ◽  
Marko Ljubotina
Keyword(s):  
Transport Properties ◽  
Quantum Systems ◽  
Theoretical Physics ◽  
Solvable Models ◽  
Many Body ◽  
Small Perturbations ◽  
One Dimensional ◽  
Quasiperiodic Potential ◽  
Quasiperiodic Systems ◽  
Small Interactions

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

scholarly journals Quantum phase slips: from condensed matter to ultracold quantum gases

2017 ◽  
Vol 375 (2108) ◽  
pp. 20160425 ◽  
Author(s):  
C. D'Errico ◽  
S. Scaffidi Abbate ◽  
G. Modugno
Keyword(s):  
Low Temperatures ◽  
Periodic Potential ◽  
Condensed Matter ◽  
Quantum Systems ◽  
Quantum Gases ◽  
Quantum Phase ◽  
One Dimensional ◽  
Quantum Phase Slips ◽  
Ultracold Quantum Gases ◽  
Phase Slips

Quantum phase slips (QPS) are the primary excitations in one-dimensional superfluids and superconductors at low temperatures. They have been well characterized in most condensed-matter systems, and signatures of their existence have been recently observed in superfluids based on quantum gases too. In this review, we briefly summarize the main results obtained on the investigation of phase slips from superconductors to quantum gases. In particular, we focus our attention on recent experimental results of the dissipation in one-dimensional Bose superfluids flowing along a shallow periodic potential, which show signatures of QPS. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

scholarly journals Quantized classical response from spectral winding topology

2021 ◽  
Author(s):  
Linhu Li ◽  
Sen Mu ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Linear Response ◽  
Condensed Matter ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Topological Invariants ◽  
Response Theory ◽  
New Paradigm ◽  
Classical Systems ◽  
State Response ◽  
Mathematical Properties

Abstract Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge modes as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

scholarly journals One-Dimensional Disordered Bosonic Systems

Atoms ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 112
Author(s):  
Chiara D’Errico ◽  
Marco G. Tarallo
Keyword(s):  
Transport Properties ◽  
Quantum Systems ◽  
Quantum Gases ◽  
Many Body ◽  
Complete Understanding ◽  
One Dimensional ◽  
Exotic States ◽  
Theoretical Predictions ◽  
Open Question

Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.

scholarly journals Entanglement spreading in non-equilibrium integrable systems

2020 ◽  
Author(s):  
Pasquale Calabrese
Keyword(s):  
Summer School ◽  
Condensed Matter ◽  
Entanglement Entropy ◽  
Interaction Strength ◽  
Quantum Systems ◽  
Equilibrium Dynamics ◽  
Thermodynamic Entropy ◽  
Short Course ◽  
Quasiparticle Picture ◽  
Non Equilibrium

These are lecture notes for a short course given at the Les Houches Summer School on ``Integrability in Atomic and Condensed Matter Physics'', in summer 2018. Here, I pedagogically discuss recent advances in the study of the entanglement spreading during the non-equilibrium dynamics of isolated integrable quantum systems. I first introduce the idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics and then join such an idea with the quasiparticle picture for the entanglement spreading to provide quantitive predictions for the time evolution of the entanglement entropy in arbitrary integrable models, regardless of the interaction strength.

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