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arXiv:2601.19152 · Physical review. B./Physical review. B

Evolution of quantum geometric tensor of 1D periodic systems after a quench

Jia-Chen Tang, Xu-Yang Hou, Yu-Huan Huang, Hao Guo. Chih-Chun Chien

quant-phcond-mat.otherSubmitted Jan 27, 2026• Announced Jan 28, 2026• 0 citations
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Abstract

We investigate the post-quench dynamics of the quantum geometric tensor (QGT) of 1D periodic systems with a suddenly changed Hamiltonian. The diagonal component with respect to the crystal momentum gives a metric corresponding to the variance of the time-evolved position, and its coefficient of the quadratic term in time is the group-velocity variance, signaling ballistic wavepacket dispersion. The other diagonal QGT component with respect to time reveals the energy variance. The off-diagonal QGT component features a real part as a covariance and an imaginary part representing a quench-induced curvature. Using the Su-Schrieffer-Heeger (SSH) model as an example, our numerical results of different quenches confirm that the post-quench QGT is governed by physical quantities and local geometric objects from the initial state and post-quench bands, such as the Berry connection, group velocities, and energy variance. Furthermore, the connections between the QGT and physical observables suggest the QGT as a comprehensive probe for nonequilibrium phenomena.

Journal reference
Physical Review B 113, 174301 (2026)
DOI
10.1103/zd1j-dlqg
Comments
12 pages, 3 figures, submitted

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We investigate the post-quench dynamics of the quantum geometric tensor (QGT) of 1D periodic systems with a suddenly changed Hamiltonian. The diagonal component with respect to the crystal momentum gives a metric corresponding to the variance of the time-evolved position, and its coefficient of the quadratic term in time is the group-velocity variance, signaling ballistic wavepacket dispersion. The other diagonal QGT component with respect to time reveals the energy variance. The off-diagonal QGT component features a real part as a covariance and an imaginary part representing a quench-induced curvature. Using the Su-Schrieffer-Heeger (SSH) model as an example, our numerical results of different quenches confirm that the post-quench QGT is governed by physical quantities and local geometric objects from the initial state and post-quench bands, such as the Berry connection, group velocities, and energy variance. Furthermore, the connections between the QGT and physical observables suggest the QGT as a comprehensive probe for nonequilibrium phenomena.
The quantum geometric tensor (QGT) fundamentally encodes the geometry and topology of quantum states in both Hermitian and non-Hermitian regimes. While adiabatic perturbation theory links its real part (quantum metric) and imaginary part (Berry curvature) to energy fluctuations and generalized forces, respectively, in Hermitian systems, direct measurement of the QGT, which is defined using both left and right eigenstates of a non-Hermitian Hamiltonian, remains challenging. Here we develop two quantum simulation schemes to directly extract all components of the QGT in pseudo-Hermitian systems with real spectra. Each scheme independently determines the complete QGT using generalized expectation values of either the energy fluctuation operator or the generalized force operator with respect to two time-evolved states prepared through distinct nonadiabatic evolutions, thereby establishing two self-contained measurement protocols. We illustrate the validity of these schemes on two qqq-deformed two-band models: one with nontrivial topology and the other with a nonvanishing off-diagonal quantum metric. Numerical simulations demonstrate that, for suitably chosen nonadiabatic ramp velocities, both schemes achieve high-fidelity agreement with theoretical predictions for measuring the QGT in both models and successfully capture the topological phase transition of the first model using Chern numbers calculated from Berry curvatures. For larger velocities, the generalized force scheme yields greater accuracy for the real part of the QGT, while the energy fluctuation scheme better captures its imaginary part. This work establishes a framework for extending dynamical measurement schemes from Hermitian to pseudo-Hermitian systems with real spectra.
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We develop a comprehensive, gauge-covariant geometric framework for non-Hermitian quantum systems in the quasi-Hermitian regime, that is, the region of parameter space where the non-Hermitian Hamiltonian admits a real spectrum and a positive-definite metric operator. We build this framework by elevating the Dyson map to a central geometric object. This map is the transformation that converts a non-Hermitian Hamiltonian into an equivalent Hermitian one. From it we construct the Dyson connection and decompose it into Hermitian and anti-Hermitian parts, identified respectively as {\it stretching } and {\it rotation } components. This decomposition cleanly separates the genuine physical metric deformations from the unitary gauge redundancies. Working with manifestly gauge-covariant states, we then derive the complex non-Hermitian Berry phase and the quantum geometric tensor (QGT), and show that the non-Hermitian geometric curvature originates from the non-commutativity of the stretching components at the operator level. We further analyse the geometric singularities near an exceptional point (EP) and uncover a distinct hierarchy of divergences. For a general two-level non-Hermitian model, the quantum metric tensor (QMT) exhibits a leading-order divergence ∼∣εμ∣−2\sim |ε_μ|^{-2}∼∣εμ​∣−2, while the Berry curvature shows a weaker, subleading divergence ∼∣εμ∣−3/2\sim |ε_μ|^{-3/2}∼∣εμ​∣−3/2, with εμε_μεμ​ denoting the parameter displacement from the EP along an individual parameter axis μμμ. Finally, we examine physical realizations of this model, including the non-Hermitian Su--Schrieffer--Heeger (SSH) and Hatano--Nelson (HN) models, where exact analytical results confirm the predicted critical scaling laws and illustrate the metric-deformation-driven non-Hermitian geometries.
The quantum geometric tensor (QGT) characterizes the local geometry of quantum states, and its components directly account for the dynamical effects observed, e.g., in condensed-matter systems. In this work, we address the problem of extending the QGT formalism to non-Hermitian systems with gain and loss. In particular, we investigate a wavepacket dynamics in two-band non-Hermitian systems to elucidate how non-Hermiticity affects the definition of QGT. We employ first-order perturbation theory to account for nonadiabatic corrections due to interband mixing. Our results suggest that two different generalizations of the QGT, one defined using only the right eigenstates and the other one using both the left and right eigenstates, both play a significant role in wavepacket dynamics. We then determine the accuracy of the perturbative approach by simulating a wavepacket dynamics in a well-studied physical non-Hermitian system—exciton polaritons in a semiconductor microcavity. Our work aids deeper understanding of quantum geometry and dynamical behavior in non-Hermitian systems.
The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the Sj\"oqvist distance is developed. The resulting Sj\"oqvist QGT is invariant under gauge transformations of individual spectrum levels of the density matrix. A Pythagorean-like relation connects the distances and gauge transformations, which clarifies the role of the parallel-transport condition. The real part of the QGT naturally decomposes into a sum of the Fisher-Rao metric and Fubini-Study metric, allowing a distinction between different contributions to the quantum distance. The imaginary part of the QGT is proportional to a weighted summation of the Berry curvatures, which leads to a geometric phase for mixed states under certain conditions. We present three examples of different dimensions to illustrate the temperature dependence of the QGT and a discussion on possible implications.