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Physica Scripta

Entanglement and avoided crossing dynamics in the disordered Majumdar-Ghosh model

Pranay Barkataki, M. S. Ramkarthik

Published May 24, 2021• 1 citation
Publisher

Abstract

Abstract We study the ground and first excited state of the finite one dimensional Majumdar-Ghosh model with quenched disorder about the avoided crossings. We find a relation between the shift of the first avoided crossing and average value of random numbers. For low disorder regime, the two-qubit, odd and even partition entanglement gets exchanged at avoided crossings for low spin, and former two for any value of spin. This effect has a deep relation with the dimerization nature of these states. We develop an expression sans entanglement measures to detect and study these crossings.

DOI
10.1088/1402-4896/ac0469

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Abstract We study the ground and first excited state of the finite one dimensional Majumdar-Ghosh model with quenched disorder about the avoided crossings. We find a relation between the shift of the first avoided crossing and average value of random numbers. For low disorder regime, the two-qubit, odd and even partition entanglement gets exchanged at avoided crossings for low spin, and former two for any value of spin. This effect has a deep relation with the dimerization nature of these states. We develop an expression sans entanglement measures to detect and study these crossings.
We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh point. There, spinons remain gapped and localize in Lifshitz states whose localization length is analytically obtained. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.
The transition from a gapless liquid to a gapped dimerized ground state that occurs in the frustrated antiferromagnetic Majumdar-Ghosh (or ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg) model is revisited from the point of view of entanglement. We study the evolution of entanglement spectra, a ``projected subspace'' block entropy, and concurrence in the Schmidt vectors through the transition. The standard tool of Schmidt decomposition along with the existence of the unique Majumdar-Ghosh (MG) point where the ground states are degenerate and known exactly suggest the projection into two orthogonal subspaces that is useful even away from this point. Of these, one is a dominant five-dimensional subspace containing the complete state at the MG point and the other contributes marginally, albeit with increasing weight as the number of spins is increased. We find that the marginally contributing subspace has a minimum von Neumann entropy in the vicinity of the dimerization transition. Entanglement content between pairs of spins in the Schmidt vectors, studied via concurrence, shows that those belonging to the dominant five-dimensional subspace display a clear progress towards dimerization as the MG point is approached. In contrast, study of the Schmidt vectors in the marginally contributing subspace, as well as in the projection of the ground state in this space, display pair concurrence which decreases on both sublattices as the MG point is approached. The robustness of these observations indicate their possible usefulness in the study of models that have similar transitions, and have hitherto been difficult to study using standard entanglement signatures.
We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behavior of the entanglement entropy characterizing the unfrustrated Heisenberg chain above ${J}_{2}\ensuremath{\approx}0.25$. This feature can be used as an indicator of the dimer phase transition occurring in this model. Additionally, we also consider entanglement at the MG point J2=0.5J1{J}_{2}=0.5{J}_{1}J2​=0.5J1​.
We study a one-dimensional Ising model with a magnetic field and show that tilting the field induces a transition to quantum chaos. We explore the stationary states of this Hamiltonian to show the intimate connection between entanglement and avoided crossings. In general, entanglement gets exchanged between the states undergoing an avoided crossing with an overall enhancement of multipartite entanglement at the closest point of approach, simultaneously accompanied by diminishing two-body entanglement as measured by concurrence. We find that both for stationary as well as nonstationary states, nonintegrability leads to a destruction of two-body correlations and distributes entanglement more globally.
We investigate the behavior of quantum correlations of paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models. We show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can become more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins--for classical and quantum correlations--is related to the quantum critical point in the corresponding ordered system.
Abstract We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1 - J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2 / J 1 ≈ 0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 1-D Heisenberg frustrated J 1 - J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2-D Heisenberg J 1 - J 2 model and Shastry-Sutherland model and find similar indications of quantum phase transitions.