On the absence of stationary currents

We review the proofs of a theorem of Bloch on the absence of macroscopic stationary currents in quantum systems. The standard proof shows that the current in 1D vanishes in the large volume limit under rather general conditions. In higher dimensions, the total current across a cross-section does not need to vanish in gapless systems but it does vanish in gapped systems. We focus on the latter claim and give a self-contained proof motivated by a recently introduced index for the many-body charge transport in quantum lattice systems having a conserved [Formula: see text]-charge.

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Hubbard-Stratonovich-like Transformations for Few-Body Interactions

EPJ Web of Conferences ◽

10.1051/epjconf/201817511012 ◽

2018 ◽

Vol 175 ◽

pp. 11012

Author(s):

Christopher Körber ◽

Evan Berkowitz ◽

Thomas Luu

Keyword(s):

Perturbation Theory ◽

Great Accuracy ◽

Quantum Systems ◽

Collective Phenomena ◽

Many Body ◽

Chiral Perturbation ◽

Body Level ◽

The Many ◽

Three Body ◽

Number Of Particles

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the an-alytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three-and more-body inter-actions, is presented.

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Predicting Imperfect Echo Dynamics in Many-Body Quantum Systems

Zeitschrift für Naturforschung A ◽

10.1515/zna-2019-0383 ◽

2020 ◽

Vol 75 (5) ◽

pp. 403-411 ◽

Cited By ~ 2

Author(s):

Lennart Dabelow ◽

Peter Reimann

Keyword(s):

Nonequilibrium State ◽

Quantum Systems ◽

Many Body ◽

Echo Signal ◽

Initial State ◽

Time Period ◽

Nonequilibrium States ◽

The Many ◽

Backward Propagation ◽

Analytic Prediction

AbstractEcho protocols provide a means to investigate the arrow of time in macroscopic processes. Starting from a nonequilibrium state, the many-body quantum system under study is evolved for a certain period of time τ. Thereafter, an (effective) time reversal is performed that would – if implemented perfectly – take the system back to the initial state after another time period τ. Typical examples are nuclear magnetic resonance imaging and polarisation echo experiments. The presence of small, uncontrolled inaccuracies during the backward propagation results in deviations of the “echo signal” from the original evolution and can be exploited to quantify the instability of nonequilibrium states and the irreversibility of the dynamics. We derive an analytic prediction for the typical dependence of this echo signal for macroscopic observables on the magnitude of the inaccuracies and on the duration τ of the process, and verify it in numerical examples.

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Many-body localization: stability and instability

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2016.0422 ◽

2017 ◽

Vol 375 (2108) ◽

pp. 20160422 ◽

Cited By ~ 26

Author(s):

Wojciech De Roeck ◽

John Z. Imbrie

Keyword(s):

Higher Dimensions ◽

Quantum Systems ◽

One Dimension ◽

Reasonable Assumption ◽

Level Spacing ◽

Weak Disorder ◽

Many Body ◽

Integrals Of Motion ◽

Stability And Instability ◽

Rare Regions

Rare regions with weak disorder (Griffiths regions) have the potential to spoil localization. We describe a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension, under a physically reasonable assumption on the statistics of eigenvalues. We discuss ideas about the situation in higher dimensions, where one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions. We argue that ergodicity is restored in dimension d >1, although equilibration should be extremely slow, similar to the dynamics of glasses. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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THE CORRELATED CROSS SECTION OF THE MANY-BODY SCATTERING

Acta Mathematica Scientia ◽

10.1016/s0252-9602(17)30823-8 ◽

1996 ◽

Vol 16 ◽

pp. 126-130

Author(s):

Zhiyong Wei ◽

Yongtai Zhu

Keyword(s):

Cross Section ◽

Many Body ◽

The Many

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Dynamical manifestations of quantum chaos: correlation hole and bulge

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2016.0434 ◽

2017 ◽

Vol 375 (2108) ◽

pp. 20160434 ◽

Cited By ~ 26

Author(s):

E. J. Torres-Herrera ◽

Lea F. Santos

Keyword(s):

Quantum Chaos ◽

Entanglement Entropy ◽

Quantum Systems ◽

Direct Access ◽

Many Body ◽

Initial State ◽

Von Neumann ◽

Interacting Systems ◽

Correlation Hole ◽

The Many

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable–chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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