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arXiv:2111.04937 · Progress of Theoretical and Experimental Physics

Lattice Lindblad simulation

Tomoya Hayata, Yoshimasa Hidaka, Arata Yamamoto

Published Mar 28, 2022• 0 citations
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Abstract

Abstract We perform real-time lattice simulation of an open quantum system based on the Schwinger–Keldysh path integral representation of the Lindblad formalism. Although the real-time simulation generally suffers from the sign problem, a few exceptional cases exist. We focus on a sign-problem-free system of a non-relativistic spinless fermion and analyze the time evolution under driving and dissipation.

DOI
10.1093/ptep/ptac062

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Abstract We perform real-time lattice simulation of an open quantum system based on the Schwinger–Keldysh path integral representation of the Lindblad formalism. Although the real-time simulation generally suffers from the sign problem, a few exceptional cases exist. We focus on a sign-problem-free system of a non-relativistic spinless fermion and analyze the time evolution under driving and dissipation.
Quantum Monte Carlo is one of the most powerful numerical tools for studying nonpeturbative properties of quantum many-body systems. However, its application to real-time problems is limited since the complex and highly-oscillating path-integral weight of the real-time evolution harms the important sampling. % , which is the notorious sign problem. In this Letter, we show that some real-time problems in open fermion systems can be simulated using the quantum Monte Carlo. To this end, we prescribe a mapping between a real-time problem in open quantum systems and a statistical problem in non-Hermitian quantum systems; for some cases, the latter can be solved without suffering from the complex measure problem. To explain our idea and demonstrate how it works, we compute the real-time evolution of fidelities in open fermion systems under dissipation.
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from a highly oscillatory phase of the path integral. In this Letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and, in principle, applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
Abstract We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.
We consider a large quantum system with spins 12\frac{1}{2}21​ whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution from an initial antiferromagnetic state of the two-dimensional Heisenberg model, which is driven to a disordered phase, not by a Hamiltonian, but by sporadic measurements or by continuous Lindblad evolution.