Subdynamics of constrained many-body systems and the theory of transport coefficients

Abstract We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.

Download Full-text

Selected applications of typicality to real-time dynamics of quantum many-body systems

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0010 ◽

2020 ◽

Vol 75 (5) ◽

pp. 421-432 ◽

Cited By ~ 2

Author(s):

Tjark Heitmann ◽

Jonas Richter ◽

Dennis Schubert ◽

Robin Steinigeweg

Keyword(s):

Gibbs State ◽

Transport Coefficients ◽

Linear Response Theory ◽

Numerical Approach ◽

Many Body ◽

Lattice Systems ◽

Initial State ◽

Time Dynamics ◽

Many Body Systems ◽

Low Dimensional

AbstractLoosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the dynamics of quantum many-body systems, called dynamical quantum typicality (DQT). In this paper, we give a brief overview of selected applications of DQT, where particular emphasis is given to questions on transport and thermalization in low-dimensional lattice systems like chains or ladders of interacting spins or fermions. For these systems, we discuss that DQT provides an efficient means to obtain time-dependent equilibrium correlation functions for comparatively large Hilbert-space dimensions and long time scales, allowing the quantitative extraction of transport coefficients within the framework of, e. g., linear response theory (LRT). Furthermore, it is discussed that DQT can also be used to study the far-from-equilibrium dynamics resulting from sudden quench scenarios, where the initial state is a thermal Gibbs state of the pre-quench Hamiltonian. Eventually, we summarize a few combinations of DQT with other approaches such as numerical linked cluster expansions or projection operator techniques. In this way, we demonstrate the versatility of DQT.

Download Full-text

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

International Journal of Modern Physics E ◽

10.1142/s021830130801194x ◽

2008 ◽

Vol 17 (supp01) ◽

pp. 304-317

Author(s):

Y. M. ZHAO

Keyword(s):

Ground State ◽

Collective Motion ◽

Regular Structure ◽

Positive Parity ◽

Many Body ◽

Random Interactions ◽

Atomic Nuclei ◽

Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

Download Full-text

Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

Physical Review Letters ◽

10.1103/physrevlett.126.110602 ◽

2021 ◽

Vol 126 (11) ◽

Author(s):

Benjamin Geiger ◽

Juan Diego Urbina ◽

Klaus Richter

Keyword(s):

Many Body ◽

Many Body Systems

Download Full-text

Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions

Physical Review Research ◽

10.1103/physrevresearch.2.023211 ◽

2020 ◽

Vol 2 (2) ◽

Cited By ~ 5

Author(s):

Davide Rossini ◽

Ettore Vicari

Keyword(s):

Many Body ◽

Quantum Transitions ◽

Many Body Systems

Download Full-text

Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

Physical Review Letters ◽

10.1103/physrevlett.125.260601 ◽

2020 ◽

Vol 125 (26) ◽

Cited By ~ 2

Author(s):

Norifumi Matsumoto ◽

Kohei Kawabata ◽

Yuto Ashida ◽

Shunsuke Furukawa ◽

Masahito Ueda

Keyword(s):

Phase Transition ◽

Continuous Phase ◽

Many Body ◽

Continuous Phase Transition ◽

Many Body Systems ◽

Gap Closing

Download Full-text

Universal relations for ultracold reactive molecules

Science Advances ◽

10.1126/sciadv.abd4699 ◽

2020 ◽

Vol 6 (51) ◽

pp. eabd4699

Author(s):

Mingyuan He ◽

Chenwei Lv ◽

Hai-Qing Lin ◽

Qi Zhou

Keyword(s):

Critical Role ◽

Interaction Strength ◽

Quantum Correlations ◽

Polar Molecules ◽

Many Body ◽

Density Correlation ◽

Ultracold Polar Molecules ◽

Unexplored Area ◽

Many Body Systems

The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.

Download Full-text

Epidemic growth and Griffiths effects on an emergent network of excited atoms

Nature Communications ◽

10.1038/s41467-020-20333-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

T. M. Wintermantel ◽

M. Buchhold ◽

S. Shevate ◽

M. Morgado ◽

Y. Wang ◽

...

Keyword(s):

Complex Systems ◽

Power Laws ◽

Excitation Density ◽

Griffiths Phase ◽

Many Body ◽

Excited Atoms ◽

Equilibrium Dynamics ◽

Many Body Systems ◽

Excitation Number ◽

Non Equilibrium

AbstractWhether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.

Download Full-text

Probing phase transitions of holographic entanglement entropy with fixed area states

Journal of High Energy Physics ◽

10.1007/jhep12(2020)084 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Donald Marolf ◽

Shannon Wang ◽

Zhencheng Wang

Keyword(s):

Phase Transitions ◽

Entanglement Entropy ◽

Many Body ◽

Btz Black Hole ◽

Holographic Entanglement Entropy ◽

Volume Limit ◽

Cutoff Dependence ◽

Diagonal Approximation ◽

Fixed Area ◽

Many Body Systems

Abstract Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain ‘diagonal approximation’ will hold. In terms of the bulk Newton constant G, this yields a correction of order O(G−1/2) near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT ‘phase transition’ into a crossover already at this level of analysis.We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS3 vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the O(G−1/2) correction found Penington et al. for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.

Download Full-text

Undecidability in quantum thermalization

Nature Communications ◽

10.1038/s41467-021-25053-0 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Naoto Shiraishi ◽

Keiji Matsumoto

Keyword(s):

Turing Machine ◽

Thermal Equilibrium ◽

General Theorem ◽

Nearest Neighbour ◽

Many Body ◽

Initial State ◽

One Dimensional ◽

Universal Turing Machine ◽

Many Body Systems ◽

Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

Download Full-text