Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics, such as the level spacing distribution, agree with those of random matrix theory (RMT). Using the example of the kicked Ising chain we demonstrate that even if both level spacing distribution and eigenvector statistics agree well with random matrix predictions, the entanglement entropy deviates from the expected RMT behavior, i.e., the Page curve. To explain this observation we propose a quantity that is based on the effective Hamiltonian of the kicked system. Specifically, we analyze the distribution of the strengths of the effective spin interactions and compare them with analytical results that we obtain for circular ensembles. Thereby we group the effective spin interactions corresponding to the number k of spins which contribute to the interaction. By this the deviations of the entanglement entropy can be attributed to significantly different behavior of the k-spin interactions compared with RMT.Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics, such as the level spacing distribution, agree with those of random matrix theory (RMT). Using the example of the kicked Ising chain we demonstrate that even if both level spacing distribution and eigenvector statistics agree well with random matrix predictions, the entanglement entropy deviates from the expected RMT behavior, i.e., the Page curve. To explain this observation we propose a quantity that is based on the effective Hamiltonian of the kicked system. Specifically, we analyze the distribution of the strengths of the effective spin interactions and compare them with analytical results that we obtain for circular ensembles. Thereby we group the effective spin interactions corresponding to the number k of spins which contribute to the interaction. By this the deviations of the entanglement entropy can be attributed to significantly different behavior of the k-spin interactions compared with RMT.

arXiv:2306.09034Physical review. EOct 12, 20234 citations

Entanglement Hamiltonians for quantum spin chains

Ronny Thomale, Stephan Rachel, Daniel P. Arovas +1 more

Bulletin of the American Physical SocietyMar 24, 20110 citations

Spectral crossovers and universality in quantum spin chains coupled to random fields

Debojyoti Kundu, Santosh Kumar, Subhra Sen Gupta

We study the spectral properties of and spectral crossovers between different random matrix ensembles [Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE)] in correlated spin-chain systems, in the presence of random magnetic fields, and the scalar spin-chirality term, competing with the usual isotropic and time-reversal invariant Heisenberg term. We have investigated these crossovers in the context of the level-spacing distribution and the level-spacing ratio distribution. We use random matrix theory (RMT) analytical results to fit the observed Poissonian-to-GOE and GOE-to-GUE crossovers, and examine the relationship between the RMT crossover parameter $\ensuremath{\lambda}$ and scaled physical parameters of the spin-chain systems in terms of a scaling exponent. We find that the crossover behavior exhibits universality, in the sense that, it becomes independent of lattice size in the large Hamiltonian matrix dimension limit. Moreover, the scaling exponent obtained from such a finite size scaling analysis, seems to be quite robust and independent of the type of crossover considered or the specific spectral correlation measure used.We study the spectral properties of and spectral crossovers between different random matrix ensembles [Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE)] in correlated spin-chain systems, in the presence of random magnetic fields, and the scalar spin-chirality term, competing with the usual isotropic and time-reversal invariant Heisenberg term. We have investigated these crossovers in the context of the level-spacing distribution and the level-spacing ratio distribution. We use random matrix theory (RMT) analytical results to fit the observed Poissonian-to-GOE and GOE-to-GUE crossovers, and examine the relationship between the RMT crossover parameter $\ensuremath{\lambda}$ and scaled physical parameters of the spin-chain systems in terms of a scaling exponent. We find that the crossover behavior exhibits universality, in the sense that, it becomes independent of lattice size in the large Hamiltonian matrix dimension limit. Moreover, the scaling exponent obtained from such a finite size scaling analysis, seems to be quite robust and independent of the type of crossover considered or the specific spectral correlation measure used.

arXiv:2309.14076Physical review. B./Physical review. BJan 21, 202210 citations

Random matrix theory universality of current operators in spin- $S$ Heisenberg chainsRandom matrix theory universality of current operators in spin-$S$ Heisenberg chains

Mariel Kempa, Markus Kraft, Robin Steinigeweg +2 more

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently narrow energy window, their statistical properties can be described by an unitarily invariant ensemble, and testable criteria have been introduced, which are based on the scaling behavior of free cumulants. In this paper, we investigate the conjecture numerically in translationally invariant Heisenberg spin chains with spin quantum number $S =\frac{1}{2},1,\frac{3}{2}$ . Combining a quantum-typicality-based numerical method with the exploitation of the system's symmetries, we study the spin current operator and find clear evidence of consistency with the proposed criteria in chaotic cases. Our findings further support the conjecture of the existence of RMT universality as manifest in the observable properties in quantum chaotic systems.Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently narrow energy window, their statistical properties can be described by an unitarily invariant ensemble, and testable criteria have been introduced, which are based on the scaling behavior of free cumulants. In this paper, we investigate the conjecture numerically in translationally invariant Heisenberg spin chains with spin quantum number $S =\frac{1}{2},1,\frac{3}{2}$. Combining a quantum-typicality-based numerical method with the exploitation of the system's symmetries, we study the spin current operator and find clear evidence of consistency with the proposed criteria in chaotic cases. Our findings further support the conjecture of the existence of RMT universality as manifest in the observable properties in quantum chaotic systems.

cond-mat.stat-mechCross-listedarXiv:2601.10211Physical review. EJan 16, 20260 citations

Entanglement in Spin Chains

K. Sengupta

arXiv:2109.02657Quantum science and technologyJan 1, 202232 citations

Random matrix theory universality of current operators in spin-

S

Heisenberg chains

S =\frac{1}{2},1,\frac{3}{2}

. Combining a quantum-typicality-based numerical method with the exploitation of the system's symmetries, we study the spin current operator and find clear evidence of consistency with the proposed criteria in chaotic cases. Our findings further support the conjecture of the existence of RMT universality as manifest in the observable properties in quantum chaotic systems.