Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions

Abstract

Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent $\alpha$. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interaction. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy level spacings, as obtained by ED for up to $N\sim 18$ spins, we find indications of a delocalization transition at ${\alpha }_c\approx 1$ in the middle of the energy spectrum. With RSRG-X and ED, we show that for $\alpha >{\alpha }^{\ast }$ the entanglement entropy (EE) of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for $\alpha <{\alpha }^{\ast }$ EE displays an algebraic growth with the subsystem size $l$, $S_l\sim l^{\beta }$, with $0<\beta <1$. We find that ${\alpha }^{\ast }\approx 1$ coincides with the delocalization transition ${\alpha }_c$ in the middle of the many-body spectrum. An interpretation of these results based on the structure of the RG rules is proposed, which is due to {\it rainbow} proliferation for very long-range interactions $\alpha \ll 1$. We also investigate the effective temperature dependence of the EE allowing us to study the half-chain entanglement entropy of eigenstates at different energy densities, where we find that the crossover in EE occurs at ${\alpha }^{\ast }<1$.

arXiv comment11 pages, 13 figures

References in corpus (40)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• Geometric and Renormalized Entropy in Conformal Field Theory
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Schrieffer-Wolff transformation for quantum many-body systems
• Strong disorder RG approach of random systems
• Entanglement entropy of random quantum critical points in one dimension
• Multifractality and critical fluctuations at the Anderson transition
• The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
• Quantum chaos: an introduction via chains of interacting spins-1/2
• Quantum criticality of hot random spin chains
• Entanglement contour
• Particle-hole symmetry, many-body localization, and topological edge modes
• Correlation amplitude and entanglement entropy in random spin chains
• Quantum dynamics of disordered spin chains with power-law interactions
• Excited-state entanglement and thermal mutual information in random spin chains
• From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
• More on the rainbow chain: entanglement, space-time geometry and thermal states
• Strongly disordered spin ladders
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Random transverse-field Ising chain with long-range interactions
• Maximally Entangled Mode, Metal-Insulator Transition and Violation of Entanglement Area Law in Non-interacting Fermion Ground States
• Unusual area-law violation in random inhomogeneous systems
• Entanglement spectrum and entangled modes of highly excited states in random XX spin chains
• Phase diagrams and universality classes of random antiferromagnetic spin ladders
• Many-body localization in XY spin chains with long-range interactions: An exact diagonalization study
• Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
• Random Antiferromagnetic Spin-1/2 Chains with Competing Interactions
• Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
• Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Quantum Chaos in the Heisenberg Spin Chain: the Effect of Dzyaloshinskii-Moriya Interaction
• Comparison between disordered quantum spin 1/2 chains

Cited by in corpus (6)

• Pair localization in dipolar systems with tunable positional disorder
• Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors
• Cluster truncated Wigner approximation for bond-disordered Heisenberg spin models
• Entanglement entropy of XX spin $1/2$ chain with random partitioning at arbitrary temperature
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Excited States and Finite Temperature Properties