Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model

Kaneko, Ryui; Danshita, Ippei

doi:10.1038/s42005-022-00848-9

Cited by 17 publications

(4 citation statements)

References 83 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the transverse (longitudinal) correlation tends to exhibit less (more) oscillations. Such effects have been intensively examined in the correlation spreading of the Bose-Hubbard model [45,48,49,102,103].…”

Section: B Results By the Lswamentioning

confidence: 99%

Dynamics of correlation spreading in low-dimensional transverse-field Ising models

Kaneko¹,

Danshita²

2023

Preprint

View full text Add to dashboard Cite

We investigate the dynamical spreading of spatial correlations after a quantum quench starting from a magnetically disordered state in the transverse-field Ising model at one (1D) and two spatial dimensions (2D). We analyze specifically the longitudinal and transverse spin-spin correlation functions at equal time with use of several methods. From the comparison of the results in 1D obtained by the linear spin-wave approximation (LSWA) and those obtained by the rigorous analytical approach, we show that the LSWA can asymptotically reproduce the exact group velocity in the limit of strong transverse fields while it fails to capture the detailed time dependence of the correlation functions. By applying the LSWA to the 2D case, in which the rigorous analytical approach is unavailable, we estimate the propagation velocity to be Ja/(2 ) at the strong-field limit, where J is the Ising interaction and a is the lattice spacing. We also utilize the tensor-network method based on the projected-entangled pair states for 2D and quantitatively compute the time evolution of the correlation functions for a relatively short time. Our findings provide useful benchmarks for quantum simulation experiments of correlation spreading and theoretical refinement of the Lieb-Robinson bound in the future.

show abstract

Section: B Results By the Lswamentioning

confidence: 99%

Dynamics of correlation spreading in low-dimensional transverse-field Ising models

Kaneko¹,

Danshita²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Typical examples include (i) noninteracting higher-dimensional systems (see Refs. [73][74][75] for correlation-spreading dynamics with a quench to U J in 2D), (ii) Anderson localization with long-range hopping (see Refs. [76] and [77] for free fermions), (iii) localization in disorder-free or correlated-disorder systems such as the Aubry-André model [78] (see Refs.…”

Section: Discussionmentioning

confidence: 99%

Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system

Kagamihara¹,

Kaneko²,

Yamashika³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We investigate the time-dependent Rényi entanglement entropy after a quantum quench starting from the Mott-insulating and charge-density-wave states in a one-dimensional free boson system. The second Rényi entanglement entropy is found to be the negative of the logarithm of the permanent of a matrix consisting of time-dependent single-particle correlation functions. From this relation and a permanent inequality, we obtain rigorous conditions for satisfying the volume-law entanglement growth. We also succeed in calculating the time evolution of the entanglement entropy in unprecedentedly large systems by brute-force computations of the permanent. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.

show abstract

“…Recent developments in iPEPS optimization [39][40][41] , contraction 42,43 , energy extrapolations 44 , and universality-class estimation [45][46][47] opened an avenue towards even more challenging problems, including simulation of thermal states [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63] , mixed states of open systems 56,64,65 , excited states 66,67 , or unitary evolution 56,[68][69][70][71][72][73][74][75][76] .…”

Section: Introductionmentioning

confidence: 99%

Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space

Dziarmaga¹

2022

Preprint

View full text Add to dashboard Cite

Time evolution of an infinite 2D many body quantum lattice system can be described by the Suzuki-Trotter decomposition applied to the infinite projected entangled pair state (iPEPS). Each Trotter gate increases the bond dimension of the tensor network, D, that has to be truncated back in a way that minimizes a suitable error measure. This paper goes beyond simplified error measures -like the one used in the full update (FU), the simple update (SU), and their intermediate neighborhood tensor update (NTU) -and directly maximizes an overlap between the exact iPEPS with the increased bond dimension and the new iPEPS with the truncated one. The optimization is performed in a tangent space of the iPEPS variational manifold. This gradient tensor update (GTU) is benchmarked by a simulation of a sudden quench of a transverse field in the 2D quantum Ising model and the quantum Kibble-Zurek mechanism in the same 2D system.

show abstract

Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model

Cited by 17 publications

References 83 publications

Dynamics of correlation spreading in low-dimensional transverse-field Ising models

Dynamics of correlation spreading in low-dimensional transverse-field Ising models

Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system

Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space

Contact Info

Product

Resources

About