Anomalous scaling of conductivity in integrable fermion systems

Prelovšek, P.; Shawish, S. El; Zotos, X.; Long, M W

doi:10.1103/physrevb.70.205129

Cited by 72 publications

(135 citation statements)

References 26 publications

(31 reference statements)

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“…(8). This completes our proof of the vanishing spin stiffness in the TL, L → ∞, for any fixed range or even distribution of S z , or any distribution of m shrinking sufficiently fast that m 2 L → 0.…”

Section: Two Exact Spin Stiffness Upper Boundsmentioning

confidence: 49%

“…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%

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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.

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Section: Two Exact Spin Stiffness Upper Boundsmentioning

confidence: 49%

Section: Introductionmentioning

confidence: 99%

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

2015

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“…is nonzero in such systems [26,38]. A recent density matrix renormalization group study suggests a generic divergence of σ dc (T ) at low temperatures with σ dc ∝ 1/T [26], different from the Fermi-liquid behavior σ dc ∝ 1/T 2 that emerges in sufficiently high dimensions [44].…”

Section: Introductionmentioning

confidence: 93%

“…Besides the question of the (divergent) zero-frequency contribution, the actual frequency dependence of the optical conductivity σ reg (ω) constitutes an equally interesting problem [26,[38][39][40]. 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.…”

Section: Introductionmentioning

confidence: 99%

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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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Ground State and Finite Temperature Lanczos Methods

Prelovšek

Bonča

2013

Springer Series in Solid-State Sciences

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111

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The present review will focus on recent development of exact-diagonalization (ED) methods that use Lanczos algorithm to transform large sparse matrices onto the tridiagonal form. We begin with a review of basic principles of the Lanczos method for computing ground-state static as well as dynamical properties. Next, generalization to finite-temperatures in the form of well established finitetemperature Lanczos method is described. The latter allows for the evaluation of temperatures T > 0 static and dynamic quantities within various correlated models. Several extensions and modification of the latter method introduced more recently are analysed. In particular, the low-temperature Lanczos method and the microcanonical Lanczos method, especially applicable within the high-T regime. In order to overcome the problems of exponentially growing Hilbert spaces that prevent ED calculations on larger lattices, different approaches based on Lanczos diagonalization within the reduced basis have been developed. In this context, recently developed method based on ED within a limited functional space is reviewed. Finally, we briefly discuss the real-time evolution of correlated systems far from equilibrium, which can be simulated using the ED and Lanczos-based methods, as well as approaches based on the diagonalization in a reduced basis.

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Anomalous scaling of conductivity in integrable fermion systems

Cited by 72 publications

References 26 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

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

Ground State and Finite Temperature Lanczos Methods

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