A simple tensor network algorithm for two-dimensional steady states.
TLDR
A tensor network method is presented that can find the steady state of 2D driven-dissipative many-body models, based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle.Abstract:
Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.read more
Citations
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Exactly Solved Models in Statistical Mechanics
TL;DR: Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944 as mentioned in this paper, and there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them.
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Spectral theory of Liouvillians for dissipative phase transitions
TL;DR: In this article, the Liouvillian spectral gap has been studied in the critical region of the steady-state density matrix and the eigenmatrix of the spectral gap.
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Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems.
Alexandra Nagy,Vincenzo Savona +1 more
TL;DR: A variational method to efficiently simulate the nonequilibrium steady state of Markovian open quantum systems based on variational Monte Carlo methods and on a neural network representation of the density matrix is developed.
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Accurate Determination of Tensor Network State of Quantum Lattice Models in Two Dimensions
TL;DR: A novel numerical method to calculate accurately physical quantities of the ground state using the tensor network wave function in two dimensions and results for the Heisenberg model on a honeycomb lattice agree well with those obtained by the quantum Monte Carlo and other approaches.
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Constructing neural stationary states for open quantum many-body systems
TL;DR: A new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems, which is dubbed as the neural stationary state ansatz, and shown to simulate various spin systems efficiently.
References
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TL;DR: A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented and it is shown that this formulation is optimal in a certain sense.
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The density-matrix renormalization group in the age of matrix product states
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The density-matrix renormalization group in the age of matrix product states
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Density-matrix algorithms for quantum renormalization groups.
TL;DR: A formulation of numerical real-space renormalization groups for quantum many-body problems is presented and several algorithms utilizing this formulation are outlined, which can be applied to almost any one-dimensional quantum lattice system, and can provide a wide variety of static properties.
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The density-matrix renormalization group
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