Full counting statistics in the spin-1/2 Heisenberg XXZ chain

Collura, Mario; Eßler, Fabian H. L.; Groha, Stefan

doi:10.1088/1751-8121/aa87dd

Cited by 34 publications

(26 citation statements)

References 55 publications

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“…The rationale for considering the particular linear combinations of two-point functions (70) is to ensure cut-off independence: the initial two-point functions L † (x)L(0) 0 and R † (x)R(0) 0 diverge as x → 0 in a way that depends on the UV cutoff. This cutoff-dependence enters the equations of motion of two-point functions via the short-distance behaviour of D θ (x, 0) in the initial condition (73).…”

Section: B Time-evolution Of Density and Phasementioning

confidence: 99%

Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium

Nieuwkerk¹,

Eßler²

2019

J. Stat. Mech.

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We derive a self-consistent time-dependent harmonic approximation for the quantum sine-Gordon model out of equilibrium and apply the method to the dynamics of tunnel-coupled one-dimensional Bose gases. We determine the time evolution of experimentally relevant observables and in particular derive results for the probability distribution of subsystem phase fluctuations. We investigate the regime of validity of the approximation by applying it to the simpler case of a nonlinear harmonic oscillator, for which numerically exact results are available. We complement our self-consistent harmonic approximation by exact results at the free fermion point of the sine-Gordon model.

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Section: B Time-evolution Of Density and Phasementioning

confidence: 99%

Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium

Nieuwkerk¹,

Eßler²

2019

J. Stat. Mech.

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“…The calculations presented here have thus two general conclusions: on the one hand, they show that semisemiclassical calculations are simple methods that are able to capture important long-time features of nonequilibrium quantum dynamics at time scales much above the microscopic time scales. On the other hand, our studies reveal the power and richness of full counting statistics and full distributions, such as P (S, t), containing precious information on correlations, equilibration and dynamics [64][65][66][67][68][69] . where {+, 0, −} stand for the eigenvalues S z = {1, 0, −1} of the particles.…”

Section: Discussionmentioning

confidence: 93%

Spin fluctuations after quantum quenches in the S=1 Haldane chain: Numerical validation of the semi-semiclassical theory

et al. 2019

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We study quantum quenches in the S = 1 Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum mechanically. We analyze the non-equilibrium time evolution of the distribution of the total spin in half of the system and compare the predictions of the semi-semiclassical theory with those of a non-Abelian time evolving block decimation (TEBD) algorithm which exploits the SU(2) symmetry. We show that while the standard semiclassical approach using the universal low energy scattering matrix cannot describe the dynamics, the hybrid semiclassical method based on the full scattering matrix gives excellent agreement with the first principles TEBD simulation. arXiv:1902.08587v1 [cond-mat.stat-mech]

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“…The FCS generating function is directly measured in iTEBD simulations [45], as explained in details, e.g., in Refs. [27,37]. The results in the thermodynamic limit for three values of ∆ > 1 and for = 200 are shown in Figure 2.…”

Section: P-2mentioning

confidence: 99%

Full counting statistics in the gapped XXZ spin chain

Calabrese

Collura

Giulio

et al. 2020

EPL

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We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse magnetisation in a large spin block of length . We found that for a subsystem of even length the full counting statistics is Gaussian, while for odd subsystems it is the sum of two Gaussian distributions. We test our analytic predictions with accurate tensor networks simulations. As a byproduct, we also obtain the symmetry (magnetisation) resolved entanglement entropies.

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Full counting statistics in the spin-1/2 Heisenberg XXZ chain

Cited by 34 publications

References 55 publications

Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium

Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium

Spin fluctuations after quantum quenches in the S=1 Haldane chain: Numerical validation of the semi-semiclassical theory

Full counting statistics in the gapped XXZ spin chain

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