Continuous phase-space methods on discrete phase spaces

Žunkovič, Bojan

doi:10.1209/0295-5075/112/10003

Cited by 4 publications

(2 citation statements)

References 48 publications

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“…This complicates explicit averaging over the initial Wigner distribution. This problem can be overcome by relating the continuous and discrete Wigner representations of spins using a gauge freedom [35].…”

Section: Gauge Freedom Of Su(2) Wigner Functions and Sampling Of Init...mentioning

confidence: 99%

Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

Mink¹,

Petrosyan²,

Fleischhauer³

2022

Preprint

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We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation (DTWA) based on Monte-Carlo sampling in a discrete phase space that improves the classical treatment by accounting for lowest-order quantum fluctuations. We provide a rigorous derivation of the DTWA by embedding it in a continuous phase space, thereby introducing a hybrid discrete-continuous truncated Wigner approximation (DCTWA). We derive a set of operator-differential mappings that yield an exact equation of motion (EOM) for the continuous SU(2) Wigner function of spins. The standard DTWA is then recovered by a systematic neglection of specific terms in this exact EOM. The hybrid approach permits us to determine the validity conditions and to gain detailed understanding of the quality of the approximation, paving the way for systematic improvements. Furthermore, we show that the continuous embedding allows for a straightforward extension of the method to open spin systems subject to dephasing, losses and incoherent drive, while preserving the key advantages of the discrete approach, such as a positive definite Wigner distribution of typical initial states. We derive exact stochastic differential equations for processes which cannot be described by the standard DTWA due to the presence of non-classical noise. We illustrate our approach by applying it to the dissipative dynamics of Rydberg excitation of one-dimensional arrays of laser-driven atoms and compare it to exact results for small systems.

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Section: Gauge Freedom Of Su(2) Wigner Functions and Sampling Of Init...mentioning

confidence: 99%

Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

Mink¹,

Petrosyan²,

Fleischhauer³

2022

Preprint

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show abstract

“…dTWA has been used for simulating Heisenberg spins [11], spin-boson models [12], Rydberg systems [13], lattices of dipolar molecules [14], as well as for investigating many-body localisation and thermalisation [15]. For increasing its accuracy, extensions and refinements of the method have been proposed [16][17][18]. Also related methods, such as the cluster truncated Wigner approximation, have shown promising results in simulating spin chains [19].…”

Section: Introductionmentioning

confidence: 99%

Quenches near criticality of the quantum Ising chain—power and limitations of the discrete truncated Wigner approximation

Czischek

Gärttner

Oberthaler

et al. 2018

Quantum Sci. Technol.

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The semi-classical discrete truncated Wigner approximation (dTWA) has recently been proposed as a simulation method for spin-1/2 systems. While it appears to provide a powerful approach which shows promising results in higher dimensions and for systems with long-range interactions, its performance is still not well understood in general. Here we perform a systematic benchmark on the one-dimensional transverse-field Ising model and point to limitations of the approximation arising after sudden quenches into the quantum critical regime. Our procedure allows to identify the limitations of the semi-classical simulations and with that to determine the regimes and questions where quantum simulators can provide information which is inaccessible to semi-classics.

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Introduction

Czischek¹

2020

Springer Theses

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Continuous phase-space methods on discrete phase spaces

Cited by 4 publications

References 48 publications

Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

Quenches near criticality of the quantum Ising chain—power and limitations of the discrete truncated Wigner approximation

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