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

2020 ◽  
Vol 75 (5) ◽  
pp. 421-432 ◽  
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.

scholarly journals Droplet tilings for rapid exploration of spatially constrained many-body systems

2021 ◽  
Vol 118 (34) ◽  
pp. e2020014118
Author(s):  
Anton Molina ◽  
Shailabh Kumar ◽  
Stefan Karpitschka ◽  
Manu Prakash
Keyword(s):  
Degrees Of Freedom ◽  
Experimental System ◽  
High Energy ◽  
Geometric Constraints ◽  
Material Behavior ◽  
Two Dimensional ◽  
Many Body ◽  
Lattice Systems ◽  
Initial State ◽  
Many Body Systems

Geometry in materials is a key concept which can determine material behavior in ordering, frustration, and fragmentation. More specifically, the behavior of interacting degrees of freedom subject to arbitrary geometric constraints has the potential to be used for engineering materials with exotic phase behavior. While advances in lithography have allowed for an experimental exploration of geometry on ordering that has no precedent in nature, many of these methods are low throughput or the underlying dynamics remain difficult to observe directly. Here, we introduce an experimental system that enables the study of interacting many-body dynamics by exploiting the physics of multidroplet evaporation subject to two-dimensional spatial constraints. We find that a high-energy initial state of this system settles into frustrated, metastable states with relaxation on two timescales. We understand this process using a minimal dynamical model that simulates the overdamped dynamics of motile droplets by identifying the force exerted on a given droplet as being proportional to the two-dimensional vapor gradients established by its neighbors. Finally, we demonstrate the flexibility of this platform by presenting experimental realizations of droplet−lattice systems representing different spin degrees of freedom and lattice geometries. Our platform enables a rapid and low-cost means to directly visualize dynamics associated with complex many-body systems interacting via long-range interactions. More generally, this platform opens up the rich design space between geometry and interactions for rapid exploration with minimal resources.

scholarly journals Undecidability in quantum thermalization

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.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

scholarly journals Quantum echo dynamics in the Sherrington-Kirkpatrick model

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Silvia Pappalardi ◽  
Anatoli Polkovnikov ◽  
Alessandro Silva
Keyword(s):  
Quantum Physics ◽  
Transverse Field ◽  
Many Body ◽  
Initial State ◽  
Large N ◽  
Semiclassical Dynamics ◽  
Long Time ◽  
Kirkpatrick Model ◽  
Ehrenfest Time ◽  
Many Body Systems

Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-N) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins N. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on N and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.

Transport Properties and Control in Low-Dimensional Quantum Many-Body Systems (abstract)

2009 ◽  
Author(s):  
Lea F. Santos ◽  
Beverly Karplus Hartline ◽  
Renee K. Horton ◽  
Catherine M. Kaicher
Keyword(s):  
Transport Properties ◽  
Many Body ◽  
Many Body Systems ◽  
Low Dimensional ◽  
And Control

scholarly journals ENTANGLEMENT PROPERTIES OF QUANTUM MANY-BODY WAVE FUNCTIONS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4041-4057
Author(s):  
J. W. CLARK ◽  
A. MANDILARA ◽  
M. L. RISTIG ◽  
K. E. KÜRTEN
Keyword(s):  
Quantum Phase Transitions ◽  
Body Wave ◽  
Wave Functions ◽  
Von Neumann Entropy ◽  
Many Body ◽  
Lattice Systems ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Many Body Systems ◽  
The One

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

scholarly journals Applications of fidelity measures to complex quantum systems

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150153 ◽  
Author(s):  
Sandro Wimberger
Keyword(s):  
Cold Atoms ◽  
Dimensional System ◽  
Many Body ◽  
Practical Applications ◽  
Dynamical Regimes ◽  
Many Body Systems ◽  
Fidelity Measures ◽  
The Stability ◽  
Low Dimensional ◽  
Quantum Motion

We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular–chaotic phase space.

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