Generalized Gibbs Ensemble and string-charge relations in nested Bethe  Ansatz

Fehér, G.; Pozsgay, Balázs

doi:10.21468/scipostphys.8.3.034

Cited by 11 publications

(12 citation statements)

References 78 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will return to the issue of quasilocal charges when we discuss the XXZ model below. However, we emphasize that these are not peculiar to the XXZ model, but are a generic feature of quantum integrable lattice models (see, for instance, an explicit construction in the SU (3)-invariant chain 102 ). The core idea behind their existence, which motivates the string-charge duality, can be justified as follows.…”

Section: The Drude Weightmentioning

confidence: 99%

Superdiffusion in spin chains

Bulchandani,

Gopalakrishnan,

Ilievski

2021

Preprint

View full text Add to dashboard Cite

This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical integrable spin chains-most famously the Heisenberg model-is anomalous. Concurrently, the framework of generalized hydrodynamics has been extended to explain some of the mechanisms underlying anomalous transport. We present what is currently understood about these mechanisms, and discuss how they resemble (and differ from) the mechanisms for anomalous transport in other contexts. We also briefly review potential transport anomalies in systems where integrability is an emergent or approximate property. We survey instances of anomalous transport and dynamics that remain to be understood.

show abstract

Section: The Drude Weightmentioning

confidence: 99%

Superdiffusion in spin chains

Bulchandani,

Gopalakrishnan,

Ilievski

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Typically the amplitudes decay exponentially with the range. The quasi-local operators play an essential role in the description of the Generalized Gibbs Ensemble of Heisenberg spin chain and related models [17,18,19,20,21,22]. There a commuting set of quasi-local charges is derived from the fused transfer matrices.…”

Section: Local and Quasi-local Operatorsmentioning

confidence: 99%

Current operators in integrable spin chains: lessons from long range deformations

Pozsgay

2020

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain type of long range deformation of the local spin chains, which was discovered and explored earlier in the context of the AdS/CFT correspondence. This method is immediately applicable also to higher rank models: as a concrete example we derive the current mean values in the SU (3)-symmetric fundamental model, solvable by the nested Bethe Ansatz. The exact results take the same form as in the Heisenberg spin chains: they involve the one-particle eigenvalues of the conserved charges and the inverse of the Gaudin matrix.

show abstract

“…The definition (8) makes sense in any finite volume, but it gives the correctQ α only if L > α. In the L → ∞ limit the operatorQ(µ) is expected to be quasi-local in some neighborhood of µ = 0, for proofs in concrete cases see [33][34][35].…”

mentioning

confidence: 99%

Algebraic Construction of Current Operators in Integrable Spin Chains

Pozsgay

2020

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

Generalized Hydrodynamics is a recent theory that describes the large scale transport properties of one dimensional integrable models. At the heart of this theory lies an exact quantum-classical correspondence, which states that the flows of the conserved quantities are essentially quasi-classical even in the interacting quantum many body models. We provide the algebraic background to this observation, by embedding the current operators of the integrable spin chains into the canonical framework of Yang-Baxter integrability. Our construction can be applied in a large variety of models including the XXZ spin chains, the Hubbard model, and even in models lacking particle conservation such as the XYZ chain. Regarding the XXZ chain we present a simplified proof of the recent exact results for the current mean values, and explain how their quasi-classical nature emerges from the exact computations.

show abstract

Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz

Cited by 11 publications

References 78 publications

Superdiffusion in spin chains

Superdiffusion in spin chains

Current operators in integrable spin chains: lessons from long range deformations

Algebraic Construction of Current Operators in Integrable Spin Chains

Contact Info

Product

Resources

About