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Quantum Information and Computation

Quqntum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

Chu-Hui Fan, XiongHeng-Na, HuangYixiao, SunZhe

Published May 1, 2013• 1 citation
Publisher

Abstract

By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the SU(2) symmetry and Z2 symmetry in this ...
DOI
10.5555/2481614.2481620

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By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the SU(2)SU(2)SU(2) symmetry and Z2Z_{2}Z2​ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.
We compute the quantum correlation [quantum discord (QD)] and the entanglement (EOF) between nearest-neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EOF and other thermodynamic quantities, spotlight the critical points associated with quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.
Abstract We have studied the ground state phases of the one-dimensional (1D) spin-1/2 anisotropic frustrated ferromagnetic model, using the numerical Lanczos method. We have focused on the quantum correlations as the concurrence and the quantum discord (QD) between the nearest neighbor (NN) and the next-nearest neighbor (NNN) spins. Numerical results show that the Tomonaga-Luttinger liquid (TLL), the even-parity dimer, and the vector chiral phases can be distinguished from each other using the long-distance quantum correlations. Specially, the critical points are explicitly detected in the first derivative of the concurrence between the nearest neighbor spins with respect to the frustration parameter.
Quantum corrections of the biquadratic interaction in the 1D spin-1/2 frustrated ferromagnetic Heisenberg model are studied. The biquadratic interaction for spin-1/2 chains is eliminated and transformed to the quadratic interaction. Doing a numerical experiment, new insight as to how the classical phases get modified on the inclusion of quantum fluctuations is provided. Observed results suggest the existence of an intermediate region in the ground state phase diagram of the frustrated ferromagnetic spin-1/2 chains with combination of dimer and chiral orders. In addition, from the quantum entanglement view point, differences between quantum phases are also obtained. The nearest neighbor spins never be entangled in the frustrated ferromagnetic chains but are entangled up to the Majumdar-Ghosh point in the frustrated antiferromagnetic chains. On the other hand, the next nearest neighbor spins in the mentioned intermediate region are entangled.
We have considered the S=1∕2S=1∕2S=1∕2 antiferromagnetic Heisenberg model in two dimensions, with an additional Ising next-nearest-neighbor interaction. Antiferromagnetic next-nearest-neighbor interactions will lead to frustration, and the system responds with flipping the spins down in the xyxyxy plane. For large next-nearest-neighbor coupling the system will order in a striped phase along the zzz axis, this phase is reached through a first-order transition. We have considered two generalizations of this model, one with random next-nearest-neighbor interactions, and one with an enlarged unit cell, where only half of the atoms have next-nearest-neighbor interactions. In both cases the transition is softened to a second-order transition separating two ordered states. In the latter case we have estimated the quantum critical exponent $\ensuremath{\beta}\ensuremath{\approx}0.25$. These two cases then represent candidate examples of deconfined quantum criticality.