High-order series expansion of non-Hermitian quantum spin models

Lenke, L.; Mühlhauser, M.; Schmidt, K. P.

doi:10.1103/physrevb.104.195137

Cited by 13 publications

(7 citation statements)

References 47 publications

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“…Many examples of non-Hermitian matrices with real eigenvalues are known for which the pc-generator still convergences. This has been observed, for instance, when using Dyson-Maleev representations of spin observables [45,46] and for spin lattices subject to a non-Hermitian staggered magnetic field [62].…”

Section: Limitations Of the Pc-generator For Non-hermitian Matricesmentioning

confidence: 75%

Efficient flow equations for dissipative systems

Gary¹,

Uhrig²

2022

Preprint

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Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. [1]. In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.

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Section: Limitations Of the Pc-generator For Non-hermitian Matricesmentioning

confidence: 75%

Efficient flow equations for dissipative systems

Gary¹,

Uhrig²

2022

Preprint

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“…Many examples of non-Hermitian matrices with real eigenvalues are known for which the pc-generator still convergences. This has been observed, for instance, when using Dyson-Maleev representations of spin observables [47,48] and for spin lattices subject to a non-Hermitian staggered magnetic field [68].…”

Section: Limitations Of the Pc-generator For Non-hermitian Matricesmentioning

confidence: 75%

“…To this end, we calculate the truncation error of all generators. We do not sort the diagonal elements for this benchmark, (68). The truncation order is denoted by (o1,o2,o3,o4) for truncation in order (1,2,3,4).…”

Section: Truncation Errormentioning

confidence: 99%

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Efficient flow equations for dissipative systems

Schmiedinghoff

Uhrig

2022

SciPost Phys.

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Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. (arXiv:2007.12044). In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.

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“…To date, a number of theoretical studies have shown that dissipation drastically alters various aspects of quantum many-body physics [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In particular, the interplay between unitary many-body dynamics and nonunitary state evolution due to dissipation leads to unconventional phase transitions [19][20][21][22][23][24][25][26], quantum critical phenomena [27][28][29][30][31][32][33], and measurement-induced entanglement transitions [34][35][36][37][38][39][40][41][42][43][44]. Experimentally, high controllability of ultracold atoms has enabled observations of novel phases and phenomena unique to open quantum systems [45][46][47][48][49][50][51]…”

Section: Introductionmentioning

confidence: 99%

Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain

et al. 2022

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We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis of a non-Hermitian XXZ spin chain as a prototypical model in one-dimensional open quantum many-body systems. Our analytic calculation is based on effective field theory with bosonization, finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution. Our numerical analysis is based on the density-matrix renormalization group generalized to non-Hermitian systems (NH-DMRG). We uncover that the model in the massless regime with weak dissipation belongs to the universality class characterized by the complex-valued TL parameter, which is related to the complex generalization of the c = 1 conformal field theory. As the dissipation strength increases, the values of the TL parameter obtained by the NH-DMRG begin to deviate from those obtained by the Bethe-ansatz analysis, indicating that the model becomes massive for strong dissipation. Our results can be tested with the two-component Bose-Hubbard system of ultracold atoms subject to two-body loss.

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High-order series expansion of non-Hermitian quantum spin models

Cited by 13 publications

References 47 publications

Efficient flow equations for dissipative systems

Efficient flow equations for dissipative systems

Efficient flow equations for dissipative systems

Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain

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