scholarly journals Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

2015 ◽  
Vol 92 (12) ◽  
Author(s):  
Moritz Binder ◽  
Thomas Barthel
Keyword(s):  
Time Evolution ◽  
Equilibrium States ◽  
Matrix Product ◽  
Thermal States

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 Real time evolution at finite temperatures with operator space matrix product states

2014 ◽  
Vol 16 (7) ◽  
pp. 073007 ◽  
Author(s):  
Iztok Pižorn ◽  
Viktor Eisler ◽  
Sabine Andergassen ◽  
Matthias Troyer
Keyword(s):  
Real Time ◽  
Time Evolution ◽  
Operator Space ◽  
Matrix Product ◽  
Matrix Product States ◽  
Space Matrix

scholarly journals Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Marko Medenjak ◽  
Vladislav Popkov ◽  
Tomaz Prosen ◽  
Eric Ragoucy ◽  
Matthieu Vanicat
Keyword(s):  
Cellular Automaton ◽  
Time Evolution ◽  
Stationary State ◽  
Finite Lattice ◽  
Matrix Product ◽  
Density Profiles ◽  
Reversible Cellular Automaton ◽  
Product Expression ◽  
Particle Current ◽  
Exact Matrix

In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and the local quench. Our main result is an exact matrix product expression of the time evolution of the probability distribution, which we use to determine the time evolution of the density profiles analytically. In the second part we study the model on a finite lattice coupled with stochastic boundaries. Once again we derive an exact matrix product expression of the stationary distribution, as well as the particle current and density profiles in the stationary state. The exact expressions reveal the existence of different phases with either ballistic or diffusive transport depending on the boundary parameters.

scholarly journals Dynamical windows for real-time evolution with matrix product states

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Ho N. Phien ◽  
Guifré Vidal ◽  
Ian P. McCulloch
Keyword(s):  
Real Time ◽  
Time Evolution ◽  
Matrix Product ◽  
Matrix Product States

scholarly journals Publisher Correction: Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

2020 ◽  
Vol 16 (2) ◽  
pp. 231-231 ◽  
Author(s):  
Mario Motta ◽  
Chong Sun ◽  
Adrian T. K. Tan ◽  
Matthew J. O’Rourke ◽  
Erika Ye ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Computer ◽  
Imaginary Time ◽  
Thermal States

scholarly journals Time evolution of Matrix Product States

2006 ◽  
Vol 8 (12) ◽  
pp. 305-305 ◽  
Author(s):  
Juan José García-Ripoll
Keyword(s):  
Time Evolution ◽  
Matrix Product ◽  
Matrix Product States

scholarly journals On the prediction of equilibrium states in homogeneous turbulence

1989 ◽  
Vol 209 ◽  
pp. 591-615 ◽  
Author(s):  
Charles G. Speziale ◽  
Nessan Mac Giolla Mhuiris
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Time Evolution ◽  
Dissipation Rate ◽  
Flow Instability ◽  
Turbulence Models ◽  
Second Order ◽  
Equilibrium States ◽  
Unstable Flow

A comparison of several commonly used turbulence models (including the K–ε model and three second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for these models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to predict equilibrium states accurately for a range of the parameter Ω/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler K–ε model for the unstable flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the K–ε model erroneously yields equilibrium states that are independent of Ω/S while the Launder, Reece & Rodi model and the Shih-Lumley model predict a flow relaminarization when Ω/S > 0.39 - a result that is contrary to numerical simulations and linear spectral analyses, which indicate flow instability for at least the range 0 [les ] Ω/S [les ] 0.5. The physical implications of the results obtained from the various turbulence models considered herein are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

scholarly journals Complexity growth of operators in the SYK model and in JT gravity

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Shao-Kai Jian ◽  
Brian Swingle ◽  
Zhuo-Yu Xian
Keyword(s):  
Black Hole ◽  
Computational Complexity ◽  
Time Evolution ◽  
Quantum Chaos ◽  
Linear Growth ◽  
Quantum Systems ◽  
Growth Behavior ◽  
Definition Of ◽  
Heisenberg Operators ◽  
Thermal States

Abstract The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times.

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