arXiv subjects

Urei Miura

Publications and source records attributed to Urei Miura.

5 recordsLinked to original sources

arXiv2026

Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

Although Arnoldi reduction of a generally non-Hermitian Hamiltonian yields an upper Hessenberg matrix rather than the tridiagonal form of Hermitian Lanczos theory, we show that a closed Toda sector survives in its diagonal and subdiagonal coefficients. For a fixed finite-dimensional Hamiltonian and a cyclic state vector deformed holomorphically, the Krylov Gram determinants are $τ$ functions of the finite two-dimensional Toda lattice, whose Flaschka variables coincide exactly with these Arnoldi coefficients. The Toda dynamics therefore closes on this sector without determining the remaining upper Hessenberg entries. The subdiagonal part of the same sector also has a direct geometric meaning: the squared subdiagonal coefficients determine both the Fubini--Study metric and the Berry curvature of holomorphic Krylov subspaces, whereas the geometric quantities associated with subspaces lost at Arnoldi breakdown cease to be defined. Along a smooth real path in the cyclic region, the Arnoldi-frame connection further provides a Hermitian tridiagonal generator of exact isospectral transport. When added to the Arnoldi matrix, this generator cancels transitions between instantaneous eigenspaces and realizes counterdiabatic driving whenever the matrix is diagonalizable with a nondegenerate spectrum.

quant-ph↗

arXiv2026

Interacting Kitaev Chain with $\mathcal{N}=1$ Supersymmetry

Lattice models with supersymmetry are known to exhibit a variety of remarkable properties that do not exist in the relativistic models. In this paper, we introduce an interacting generalization of the Kitaev chain of Majorana fermions with $\mathcal{N} = 1$ supersymmetry and investigate its low-energy properties, paying particular attention to the ground-state degeneracy and low-lying fermionic excitations. First, we establish the existence of a phase with spontaneously broken supersymmetry and a phase transition out of it with the help of variational arguments and the exact ground state. We then develop, based on the superfield formalism, a simple mean-field theory, in which the order parameters detect supersymmetry-breaking, to understand the ground-state phases and low-lying Nambu-Goldstone fermions. At the solvable point ({\em frustration-free point}), the exact ground state of an open chain exhibits large degeneracy of the order of the system size, which is attributed to the existence of a zero-energy domain wall (dubbed kink or skink) separating the topological and trivial states of Majorana fermions. Our results may shed new light on the intriguing ground-state properties of supersymmetric lattice models.

cond-mat.str-el↗

arXiv2026

Exact steady states and fragmentation-induced relaxation in the no-passing asymmetric simple exclusion process

We introduce a multispecies generalization of the asymmetric simple exclusion process with a "no-passing" constraint, forbidding overtaking, on a one-dimensional reflecting (closed) chain without particle reservoirs. This no-passing rule fragments the Hilbert space into an exponential number of disjoint sectors labeled by the particle species sequence, leading to relaxation dynamics that depend sensitively on the initial ordering. We construct exact matrix-product steady states in every particle species sequence sector and derive closed-form expressions for the particle-number distribution and two-point particle correlation functions. In the two-species case, we identify a parameter regime where some sectors have finite relaxation times while others exhibit metastable relaxation dynamics, revealing the coexistence of fast and slow dynamics and strong dependence on the particle species sequence sector. Our results uncover a novel mechanism for nonequilibrium metastability arising from Hilbert space fragmentation in exclusion processes.

cond-mat.stat-mech↗

arXiv2026

Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry

We investigate the emergence of spacetime supersymmetry (SUSY) in an interacting Kitaev chain model with explicit microscopic $\mathcal{N}=1$ quantum mechanical SUSY. As the interaction strength is varied, the model transitions from a weak-coupling gapless phase with spontaneously broken SUSY to a strong-coupling phase with restored SUSY. In this paper, we numerically determine the transition point and investigate the phase structure around it. The weak-coupling phase is governed by the Ising conformal field theory (CFT) with central charge $c=1/2$, which agrees with the prediction made in our previous paper. At the SUSY restoration transition, which borders the strong-coupling gapped phase, the transition belongs to the $c=7/10$ tricritical Ising universality with emergent superconformal invariance. Crucially, the phase structure around the transition closely aligns with the scenario proposed by Zamolodchikov and others based on the integrable deformation of CFTs. These findings provide a concrete example of a lattice model where explicit microscopic supersymmetry at criticality enriches the understanding of phase transitions governed by supersymmetric conformal field theories.

cond-mat.str-el↗

arXiv2023

Supersymmetry Breaking in a Generalized Nicolai Model with Fermion Pairing

We introduce a supersymmetric lattice fermion model that contains both fermion pairing and the interacting Nicolai model. This model possesses a single control parameter, $g$, introduced through the anticommutator of the supersymmetry generators (supercharge), and it is shown that supersymmetry is broken in both finite and infinite systems as long as $g$ is finite. Additionally, the single-mode approximation is employed to establish an upper bound on the dispersion relation of Nambu-Goldstone (NG) fermions, demonstrating their gaplessness. Finally, it is shown, through numerical and analytic calculations, that the anticipated extensive ground-state degeneracy and a zero-energy flat band does not occur for generic values of the parameter $g$.

cond-mat.str-el↗