Fluctuations and non-Hermiticity in the stochastic approach to quantum spins. (English) Zbl 1519.82111
Summary: We investigate the non-equilibrium dynamics of isolated quantum spin systems via an exact mapping to classical stochastic differential equations. We show that one can address significantly larger system sizes than recently obtained, including two-dimensional systems with up to 49 spins. We demonstrate that the results for physical observables are in excellent agreement with exact results and alternative numerical techniques where available. We further develop a hybrid stochastic approach involving matrix product states. In the presence of finite numerical sampling, we show that the non-Hermitian character of the stochastic representation leads to the growth of the norm of the time-evolving quantum state and to departures for physical observables at late times. We demonstrate approaches that correct for this and discuss the prospects for further development.
MSC:
| 82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
Software:
ITensorReferences:
| [1] | Friedenauer A, Schmitz H, Glueckert J T, Porras D and Schaetz T 2008 Nat. Phys.4 757 · doi:10.1038/nphys1032 |
| [2] | Simon J, Bakr W S, Ma R, Tai M E, Preiss P M and Greiner M 2011 Nature472 307 · doi:10.1038/nature09994 |
| [3] | Meinert F, Mark M J, Kirilov E, Lauber K, Weinmann P, Daley A J and Nägerl H-C 2013 Phys. Rev. Lett.111 053003 · doi:10.1103/physrevlett.111.053003 |
| [4] | Jurcevic P, Lanyon B P, Hauke P, Hempel C, Zoller P, Blatt R and Roos C F 2014 Nature511 202 · doi:10.1038/nature13461 |
| [5] | Polkovnikov A, Sengupta K, Silva A and Vengalattore M 2011 Rev. Mod. Phys.83 863 · doi:10.1103/revmodphys.83.863 |
| [6] | Eisert J, Friesdorf M and Gogolin C 2015 Nat. Phys.11 124 · doi:10.1038/nphys3215 |
| [7] | Essler F H L and Fagotti M 2016 J. Stat. Mech. 064002 · Zbl 1456.82585 · doi:10.1088/1742-5468/2016/06/064002 |
| [8] | Calabrese P, Essler F H L and Fagotti M 2012 J. Stat. Mech. P07016 · doi:10.1088/1742-5468/2012/07/p07016 |
| [9] | Caux J S and Essler F H L 2013 Phys. Rev. Lett.110 257203 · doi:10.1103/physrevlett.110.257203 |
| [10] | Pozsgay B 2013 J. Stat. Mech. P10028 · Zbl 1456.82067 · doi:10.1088/1742-5468/2013/10/p10028 |
| [11] | Fagotti M, Collura M, Essler F H L and Calabrese P 2014 Phys. Rev. B 89 125101 · doi:10.1103/physrevb.89.125101 |
| [12] | Piroli L, Pozsgay B and Vernier E 2017 J. Stat. Mech. 023106 · Zbl 1456.81469 · doi:10.1088/1742-5468/aa5d1e |
| [13] | Piroli L, Pozsgay B and Vernier E 2018 Nucl. Phys. B 933 454 · Zbl 1395.82135 · doi:10.1016/j.nuclphysb.2018.06.015 |
| [14] | Vidal G 2004 Phys. Rev. Lett.93 040502 · doi:10.1103/physrevlett.93.040502 |
| [15] | Haegeman J, Cirac J I, Osborne T J, Pižorn I, Verschelde H and Verstraete F 2011 Phys. Rev. Lett.107 070601 · doi:10.1103/physrevlett.107.070601 |
| [16] | Rigol M, Dunjko V, Yurovsky V and Olshanii M 2007 Phys. Rev. Lett.98 050405 · doi:10.1103/physrevlett.98.050405 |
| [17] | Alba V 2015 Phys. Rev. B 91 155123 · doi:10.1103/physrevb.91.155123 |
| [18] | Hallam A, Morley J and Green A G 2019 Nat. Commun.10 2708 · doi:10.1038/s41467-019-10336-4 |
| [19] | Barry D W and Drummond P D 2008 Phys. Rev. A 78 052108 · doi:10.1103/physreva.78.052108 |
| [20] | Wurtz J, Polkovnikov A and Sels D 2018 Ann. Phys., NY395 341 · Zbl 1394.82013 · doi:10.1016/j.aop.2018.06.001 |
| [21] | Heyl M, Polkovnikov A and Kehrein S 2013 Phys. Rev. Lett.110 135704 · doi:10.1103/physrevlett.110.135704 |
| [22] | Jurcevic P et al 2017 Phys. Rev. Lett.119 080501 · doi:10.1103/physrevlett.119.080501 |
| [23] | Hogan P M and Chalker J T 2004 J. Phys. A: Math. Gen.37 11751 · Zbl 1064.82023 · doi:10.1088/0305-4470/37/49/002 |
| [24] | Galitski V 2011 Phys. Rev. A 84 012118 · doi:10.1103/physreva.84.012118 |
| [25] | Ringel M and Gritsev V 2013 Phys. Rev. A 88 062105 · doi:10.1103/physreva.88.062105 |
| [26] | De Nicola S, Doyon B and Bhaseen M J 2019 J. Phys. A: Math. Theor.52 05LT02 · Zbl 1422.82014 · doi:10.1088/1751-8121/aaf9be |
| [27] | De Nicola S, Doyon B and Bhaseen M J 2020 J. Stat. Mech. 013106 · Zbl 1459.82159 · doi:10.1088/1742-5468/ab6093 |
| [28] | Zaletel M P, Mong R S K, Karrasch C, Moore J E and Pollmann F 2015 Phys. Rev. B 91 165112 · doi:10.1103/physrevb.91.165112 |
| [29] | Wei J and Norman E 1963 J. Math. Phys.4 575 · Zbl 0133.34202 · doi:10.1063/1.1703993 |
| [30] | Kolokolov I V 1986 Phys. Lett. A 114 99 · doi:10.1016/0375-9601(86)90488-3 |
| [31] | Klimov A B and Chumakov S M 2009 A Group-Theoretical Approach to Quantum Optics: Models of Atom-Field Interactions (New York: Wiley) · doi:10.1002/9783527624003 |
| [32] | Rümelin W 1982 SIAM J. Numer. Anal.19 604 · Zbl 0496.65038 · doi:10.1137/0719041 |
| [33] | Klöden P E and Platen E 1992 Numerical Solution of Stochastic Differential Equations (Berlin: Springer) · Zbl 0752.60043 · doi:10.1007/978-3-662-12616-5 |
| [34] | Ng R, Sørensen E S and Deuar P 2013 Phys. Rev. B 88 144304 · doi:10.1103/physrevb.88.144304 |
| [35] | Weinberg P and Bukov M 2019 SciPost Phys.7 020 · doi:10.21468/scipostphys.7.2.020 |
| [36] | Fishman M, White S R and Stoudenmire E M 2020 ITensor Library version 2.1.1 (arXiv:2007.14822) |
| [37] | Rahav S, Gilary I and Fishman S 2003 Phys. Rev. A 68 013820 · doi:10.1103/physreva.68.013820 |
| [38] | Drummond P D and Gardiner C W 1980 J. Phys. A: Math. Gen.13 2353 · doi:10.1088/0305-4470/13/7/018 |
| [39] | Schollwöck U 2011 Ann. Phys., NY326 96 · Zbl 1213.81178 · doi:10.1016/j.aop.2010.09.012 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
