Entanglement spectrum and entangled modes of highly excited states in random XX spin chains

Abstract

We examine the real space renormalization group method of finding \textit{excited eigenstate} (RSRG-X) of the XX spin-1/2 chain, from entanglement perspectives. Eigenmodes of entanglement Hamiltonian, especially the maximally entangled mode and corresponding entanglement energies are studied and compared with predictions of RSRG-X. Our numerical results demonstrate the accuracy of the RSRG-X method in the strong disorder limit, and quantify its error when applied to weak disorder regime. Overall, our results validate the RSRG-X method qualitatively, but also show that its accuracy decreases with increasing temperature.

9 pages, 10 figures (one figure added)

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• Many body localization and thermalization in quantum statistical mechanics
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum criticality of hot random spin chains
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems

Cited by in corpus (23)

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• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• Strong Disorder Real-Space Renormalization for the Many-Body-Localized phase of random Majorana models
• Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Universal crossover from ground state to excited-state quantum criticality
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
• Periodically driven random quantum spin chains : Real-Space Renormalization for Floquet localized phases
• Level repulsion exponent $\beta$ for Many-Body Localization Transitions and for Anderson Localization Transitions via Dyson Brownian Motion
• Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions
• Phenomenology of many-body localization in bond-disordered spin chains
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Schmidt gap in random spin chains
• Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$
• Entanglement entropy of XX spin $1/2$ chain with random partitioning at arbitrary temperature
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Single-particle Entanglement of the Entanglement Hamiltonian Eigen-modes