Conservation laws, integrability, and transport in one-dimensional quantum systems

Sirker, Jesko; Pereira, Rodrigo G.; Affleck, Ian

doi:10.1103/physrevb.83.035115

Cited by 203 publications

(295 citation statements)

References 83 publications

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“…On the other hand, the studies of Ref. [12] show that transport at finite temperatures is dominated by a diffusive contribution, the spin stiffness being very small or zero. Such studies exclude the large spin stiffness found in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…However, the isotropic point at ∆ = 1 (the spin-1/2 XXX model) [33] is the most experimentally relevant for the spin-lattice relaxation rate and other physical quantities [12,22,23]. It is also the case that poses the most challenging technical problems for theory.…”

Section: Introductionmentioning

confidence: 99%

“…One-dimensional (1D) correlated lattice systems with L sites show exotic spin transport properties at finite temperature T > 0 whose nature has been a problem of long-standing both theoretical [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and experimental [21][22][23][24][25][26][27] interest. Often integrable quantum systems show dissipationless ballistic transport behavior.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Vanishing spin stiffness in the spin-12Heisenberg chain for any nonzero temperature

2015

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Whether at zero spin density m = 0 and finite temperatures T > 0 the spin stiffness of the spin-1/2 XXX chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an exact upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m and show that it is proportional to m 2 L in the thermodynamic limit of chain length L → ∞, for any finite, nonzero temperature. Moreover, we explicitly compute the stiffness at m = 0 and confirm that it vanishes. This allows us to exactly exclude the possibility of ballistic transport within the canonical ensemble for T > 0.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vanishing spin stiffness in the spin-12Heisenberg chain for any nonzero temperature

2015

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“…However, it is important to note that D(t) yields no information beyond the mere width of density profiles. It is also worth pointing out in that D(t) addresses the overall dynamics and does not distinguish between transport channels with potentially different behavior [84,85].…”

Section: Diffusionmentioning

confidence: 99%

Real-time dynamics of typical and untypical states in nonintegrable systems

Richter¹,

Jin²,

Raedt³

et al. 2018

Phys. Rev. B

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Understanding (i) the emergence of diffusion from truly microscopic principles continues to be a major challenge in experimental and theoretical physics. At the same time, isolated quantum many-body systems have experienced an upsurge of interest in recent years. Since in such systems the realization of a proper initial state is the only possibility to induce a nonequilibrium process, understanding (ii) the largely unexplored role of the specific realization is vitally important. Our work reports a substantial step forward and tackles the two issues (i) and (ii) in the context of typicality, entanglement as well as integrability and nonintegrability. Specifically, we consider the spin-1/2 XXZ chain, where integrability can be broken due to an additional next-nearest neighbor interaction, and study the real-time and real-space dynamics of nonequilibrium magnetization profiles for a class of pure states. Summarizing our main results, we show that signatures of diffusion for strong interactions are equally pronounced for the integrable and nonintegrable case. In both cases, we further find a clear difference between the dynamics of states with and without internal randomness. We provide an explanation of this difference by a detailed analysis of the local density of states.

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“…Some insight can be gained from effective low-energy theories such as bosonization [41][42][43], which is, however, limited to very low temperatures and may not correctly capture effects due to integrability without fine-tuning of parameters. An exact diagonalization study observed strong anomalous finitesize effects in σ reg (ω) of integrable Mott insulators [38], while many studies conclude that the dc conductivity…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature charge transport in the one-dimensional Hubbard model

et al. 2015

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We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of η 0.3.

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Conservation laws, integrability, and transport in one-dimensional quantum systems

Cited by 203 publications

References 83 publications

Vanishing spin stiffness in the spin-12Heisenberg chain for any nonzero temperature

Vanishing spin stiffness in the spin-12Heisenberg chain for any nonzero temperature

Real-time dynamics of typical and untypical states in nonintegrable systems

Finite-temperature charge transport in the one-dimensional Hubbard model

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