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arXiv:1508.05829 · Physical Review B

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

Mohammad Pouranvari, Kun Yang

Published Dec 28, 2015• 25 citations
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Abstract

We examine the real space renormalization group method of finding the excited eigenstates (RSRG-X) of the $XX$ spin-1/2 chain from entanglement perspectives. The eigenmodes of the entanglement Hamiltonian, especially the maximally entangled mode and the corresponding entanglement energies are studied and compared with the 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 the weak-disorder regime. Overall, our results validate the RSRG-X method qualitatively, but also show that its accuracy decreases with increasing temperature.

DOI
10.1103/physrevb.92.245134

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We examine the real space renormalization group method of finding the excited eigenstates (RSRG-X) of the XXXXXX spin-1/2 chain from entanglement perspectives. The eigenmodes of the entanglement Hamiltonian, especially the maximally entangled mode and the corresponding entanglement energies are studied and compared with the 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 the weak-disorder regime. Overall, our results validate the RSRG-X method qualitatively, but also show that its accuracy decreases with increasing temperature.
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Entanglement properties of excited eigenstates (or of thermal mixed states) are difficult to study with conventional analytical methods. We approach this problem for random spin chains using a recently developed real-space renormalization group technique for excited states (``RSRG-X''). For the random XX and quantum Ising chains, which have logarithmic divergences in the entanglement entropy of their (infinite-randomness) critical ground states, we show that the entanglement entropy of excited eigenstates retains a logarithmic divergence while the mutual information of thermal mixed states does not. However, in the XX case the coefficient of the logarithmic divergence extends from the universal ground-state value to a universal interval due to the degeneracy of excited eigenstates. These models are noninteracting in the sense of having free-fermion representations, allowing strong numerical checks of our analytical predictions.
Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian dephasing) remains largely unexplored. The interplay between measurements and unitary dynamics gives rise to novel phases and phase transitions in monitored quantum systems. In this work, we investigate the disordered XX spin chain subject to stochastic local measurements in the XXX and YYY bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.
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We propose an entanglement-based algorithm of the tensor-network strong-disorder renormalization group (tSDRG) method for quantum spin systems with quenched randomness. In contrast to the previous tSDRG algorithm based on the energy spectrum of renormalized block Hamiltonians, we directly utilize the entanglement structure associated with the blocks to be renormalized. We examine accuracy of the algorithm for the random antiferromagnetic Heisenberg models on one-dimensional, triangular, and square lattices. We then find that the entanglement-based tSDRG achieves better accuracy than the previous one for the square-lattice model with weak randomness, while it is less efficient for the one-dimensional and triangular-lattice models particularly in the strong-randomness region. The theoretical background and possible improvements of the algorithm are also discussed.