Theory of anomalous full counting statistics in anisotropic spin chains

Gopalakrishnan, Sarang; Morningstar, Alan; Vasseur, Romain; Khemani, Vedika

doi:10.48550/arxiv.2203.09526

Cited by 8 publications

(13 citation statements)

References 49 publications

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“…According to a phenomenological hydrody-namic picture proposed in Ref. [142], the statistics of the transferred charge, computed in equilibrium at vanishing density of magnetization, appears to match the M-Wright distribution derived earlier in Ref. [74] in the hardcore automaton (now established as one of the key universal properties of charged single-file systems studied in this work).…”

Section: Discussionsupporting

confidence: 77%

“…allowing us to express I c (j c ) through marginalization, I c (j c ) = inf jp {I c,p (j c , j p )}, (142) namely by minimizing the joint rate function over the domain J of time-integrated rescaled particle current j p , with j c kept fixed. By exploiting the fact that |j c | ≤ |j p |, we split J into two disjoint intervals J ± such that J = J − ∪ J + .…”

Section: Appendix A: Dressing the Moment Generating Functionmentioning

confidence: 99%

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Universal anomalous fluctuations in charged single-file systems

Krajnik¹,

Schmidt²,

Pasquier³

et al. 2022

Preprint

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Conventional classification of dynamical phenomena is based on universal hydrodynamic relaxation characterized by algebraic dynamical exponents and asymptotic scaling of the dynamical structure factor. This work uncovers a novel type of dynamical universality reflected in statistical properties of macroscopic fluctuating observables such as the transmitted charge. By considering a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore charged particles, we demonstrate that stringent dynamical constraints give rise to universal anomalous statistics of cumulative charge currents manifested both on the timescale characteristic of typical fluctuations and also in the rate function describing rare events. By computing the full counting statistics of net transferred charge between two extended subsystems, we establish a number of unorthodox dynamical properties in an analytic fashion. Most prominently, typical fluctuations in equilibrium are governed by a universal distribution that markedly deviates from the expected Gaussian statistics, whereas large fluctuations are described by an exotic large-deviation rate function featuring an exceptional triple critical point. Far from equilibrium, competition between dynamical phases leads to dynamical phase transitions of first and second order. Despite dynamical criticality, we find the large-deviation rate function of the joint particle-charge transfer obeys the fluctuation relation. Curiously, the univariate charge-current rate function experiences a spontaneous breaking of fluctuation symmetry upon varying the particle and charge densities in a nonequilibrium initial state. The rich phenomenology of the outlined dynamical universality is exemplified on an exactly solvable classical cellular automaton of charged hardcore particles. We determine the dynamical phase diagram in the framework of Lee-Yang's theory of phase transitions and exhibit a hyper-dimensional diagram of distinct dynamical regimes.

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Section: Discussionsupporting

confidence: 77%

Section: Appendix A: Dressing the Moment Generating Functionmentioning

confidence: 99%

Universal anomalous fluctuations in charged single-file systems

Krajnik¹,

Schmidt²,

Pasquier³

et al. 2022

Preprint

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show abstract

“…We further point out a connection to anomalous current correlations recently reported for the XXZ chain, the XNOR circuit, and for a deterministic classical automaton, Refs. [84,85]. Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Ref. [84] provides a picture in which such correlations are effectively due to the tracer motion of a single domain wall. We expect that the same arguments, and thus the presence of anomalous correlations, apply in any system with a conserved pattern, which includes Ref.…”

Section: Discussionmentioning

confidence: 99%

Emergent tracer dynamics in constrained quantum systems

Feldmeier,

Witczak-Krempa,

Knap

2022

Preprint

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We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice subjected to constrained spin interactions, such that some or even all multipole moments of the effective spin pattern formed by the particles are conserved. On the one hand, when all moments-and thus the entire spin pattern-are conserved, dynamical spin correlations reduce to tracer motion identically, generically yielding a subdiffusive dynamical exponent z = 4. This provides a common framework to understand the dynamics of several constrained lattice models, including models with XNOR or tJz -constraints. We consider random unitary circuit dynamics with such a conserved spin pattern and use the tracer picture to obtain exact expressions for their late-time dynamical correlations. Our results can also be extended to integrable quantum many-body systems that feature a conserved spin pattern but whose dynamics is insensitive to the pattern, which includes for example the folded XXZ spin chain. On the other hand, when only a finite number of moments of the pattern are conserved, the dynamics is described by a convolution of the internal hydrodynamics of the spin pattern with a tracer distribution function. As a consequence, we find that the tracer universality is robust in generic systems if at least the quadrupole moment of the pattern remains conserved. In cases where only total magnetization and dipole moment of the pattern are constant, we uncover an intriguing coexistence of two processes with equal dynamical exponent but different scaling functions, which we relate to phase coexistence at a first order transition.

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“…However, these results describe only the large time limit for large system sizes, and generally they lack a completely rigorous proof. Furthermore, they don't provide access to certain exotic features of the dynamics, such as anomalous current fluctuations [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Sublattice entanglement in an exactly solvable anyonlike spin ladder

Pozsgay

Hutsalyuk²,

Pristyák³

et al. 2022

Phys. Rev. E

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We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sub-lattices), such that the scattering phases are constants: particles of the same type scatter as free fermions, whereas the inter-particle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sub-lattice entanglement by numerical means.

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Theory of anomalous full counting statistics in anisotropic spin chains

Cited by 8 publications

References 49 publications

Universal anomalous fluctuations in charged single-file systems

Universal anomalous fluctuations in charged single-file systems

Emergent tracer dynamics in constrained quantum systems

Sublattice entanglement in an exactly solvable anyonlike spin ladder

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