The Loschmidt Index

Liska, Diego; Gritsev, Vladimir

doi:10.21468/scipostphys.10.5.100

Cited by 8 publications

(3 citation statements)

References 46 publications

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“…In the Hermitian case, the quantum metric [58] is a gauge invariant and measurable quantity [59][60][61] that can be seen as a momentum-space Riemannian metric. [62][63][64][65] It has been shown that g 𝜇𝜈 plays a central role in Chern insulators, [66][67][68][69] spreading of the Wannier functions, [70] superconducting weight in flatband superconductors, [71][72][73][74] topological semimetals, [75][76][77][78] quantum phase transitions [79][80][81] and in the semiclassical equations for wave-packets. [82] Moreover, the non-Hermitian version of the quantum metric has been originally introduced in Ref.…”

Section: Band Geometry and Topology For Dcbmentioning

confidence: 99%

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Martínez‐Strasser,

Herrera,

García‐Etxarri

et al. 2023

Adv Quantum Tech

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The spectral properties of a non‐Hermitian quasi‐1D lattice in two of the possible dimerization configurations are investigated. Specifically, it focuses on a non‐Hermitian diamond chain that presents a zero‐energy flat band. The flat band originates from wave interference and results in eigenstates with a finite contribution only on two sites of the unit cell. To achieve the non‐Hermitian characteristics, the system under study presents non‐reciprocal hopping terms in the chain. This leads to the accumulation of eigenstates on the boundary of the system, known as the non‐Hermitian skin effect. Despite this accumulation of eigenstates, for one of the two considered configurations, it is possible to characterize the presence of non‐trivial edge states at zero energy by a real‐space topological invariant known as the biorthogonal polarization. This work shows that this invariant, evaluated using the destructive interference method, characterizes the non‐trivial phase of the non‐Hermitian diamond chain. For the second non‐Hermitian configuration, there is a finite quantum metric associated with the flat band. Additionally, the system presents the skin effect despite the system having a purely real or imaginary spectrum. The two non‐Hermitian diamond chains can be mapped into two models of the Su‐Schrieffer‐Heeger chains, either non‐Hermitian, and Hermitian, both in the presence of a flat band. This mapping allows to draw valuable insights into the behavior and properties of these systems.

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Section: Band Geometry and Topology For Dcbmentioning

confidence: 99%

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Martínez‐Strasser,

Herrera,

García‐Etxarri

et al. 2023

Adv Quantum Tech

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show abstract

“…where µ, ν = q, p. It may be meaningful that the Fubini-Study metric is intimately related to the Berry curvature through a quantum geometric tensor (QGT) [40][41][42][43].…”

Section: Dgcmmentioning

confidence: 99%

Structural analysis of a collective subspace in the dynamical generator coordinate method

Hizawa¹

2022

Preprint

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In nuclear theory, the generator coordinate method (GCM), a type of configuration mixing method, is often used for the microscopic description of collective motions. However, the GCM has a problem that a structure of the collective subspace, which is the Hilbert space spanned by the configurations, is not generally understood. In this paper, I investigate the structure of the collective subspace in the dynamical GCM (DGCM), an improved version of the GCM. I then show that it is restricted to a specific form that combines tensor products and direct sums under reasonable conditions. By imposing additional specific conditions that are feasible in actual numerical calculations, it is possible to write the collective subspace as a simple tensor product of the collective part and the others. These discussions are not dependent on the details of the function space used for generating the configurations and can be applied to various methods, including the mean-field theory. Moreover, this analytical technique can also be applied to a variation after projection method (VAP), then which reveals that under a specific condition, the function space of the VAP has an untwisted structure. These consequences can provide powerful tools for discussing the collective motions with the DGCM or the GCM.

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“…When the phase driving parameter is quenched across an underlying equilibrium phase transition point, a series of zero points of LE emerge at some critical times. In general, exact zeros of LE only occur when the system size tends to infinity 1,23,24 . Meanwhile, LE always approaches to zero in the thermodynamical limit even when the quench parameter does not cross the transition point.…”

Section: Introductionmentioning

confidence: 99%

Dynamical singularity of the rate function for quench dynamics in finite size quantum systems

Zeng¹,

Zhou²,

Chen³

2022

Preprint

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The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of Loschmidt echo in the thermodynamical limit. In general, exact zeros of Loschmidt echo are not accessible in a finite size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of dynamical singularity of the rate function for finite size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite size system is divergent at a series of critical times. We demonstrate our scheme by considering the Su-Schrieffer-Heeger model and the Creutz model as concrete examples. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.

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The Loschmidt Index

Cited by 8 publications

References 46 publications

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Structural analysis of a collective subspace in the dynamical generator coordinate method

Dynamical singularity of the rate function for quench dynamics in finite size quantum systems

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