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Register a new userOn the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions
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Authors
M. A. Yurischev
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The anisotropic Heisenberg two-spin-1/2 model in an inhomogeneous magnetic field with both antisymmetric Dzyaloshinsky-Moriya and symmetric Kaplan-Shekhtman-Entin-Wohlman-Aharony cross interactions is considered at thermal equilibrium. Using a group-theoretical approach, we find fifteen spin Hamiltonians and as many corresponding Gibbs density matrices (quantum states) whose eigenvalues are expressed only through square radicals. We also found local unitary transformations that connect nine of this fifteen state collection, and one of them is the X quantum state. Since such quantum correlations as quantum entanglement, quantum discord, one-way quantum work deficit, and others are known for the X state, this allows to get the quantum correlations for any member from the nine state family. Further, we show that the remaining six quantum states are separable, that they are also connected by local unitary transformations, but, however, now the case with known correlations beyond entanglement is generally not available.
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In order to explore the effect of external temperature $T$ in quantum correlation we compute thermal entanglement and thermal discord analytically in the Heisenberg $X$ $Y$ $Z$ model with Dzyaloshinskii-Moriya Interaction term ${bm D} cdot left( {bm sigma}_1 times {bm sigma}_2 right)$. For the case of thermal entanglement it is shown that quantum phase transition occurs at $T = T_c$ due to sudden death phenomenon. For antiferromagnetic case the critical temperature $T_c$ increases with increasing $|{bm D}|$. For ferromagnetic case, however, $T_c$ exhibits different behavior in the regions $|{bm D}| geq |{bm D_*}|$ and $|{bm D}| < |{bm D_*}|$, where ${bm D_*}$ is particular value of ${bm D}$. It is shown that $T_c$ becomes zero at $|{bm D}| = |{bm D_*}|$. We explore the behavior of thermal discord in detail at $T approx T_c$. For antiferromagnetic case the external temperature makes the thermal discord exhibit exponential damping behavior, but it never reaches to exact zero. For ferromagnetic case the thermal entanglement and thermal discord are shown to be zero simultaneously at $T_c = 0$ and $|{bm D}| = |{bm D_*}|$. This is unique condition for simultaneous disappearance of thermal entanglement and thermal discord in this model.
We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.
We study the dynamics of microscopic quantum correlations, viz., bipartite entanglement and quantum discord between nearest neighbor sites, in Ising spin chain with a periodically varying external magnetic field along the transverse direction. Quantum correlations exhibit periodic revivals with the driving cycles in the finite-size chain. The time of first revival is proportional to the system size and is inversely proportional to the maximum group velocity of Floquet quasi-particles. On the other hand, the local quantum correlations in the infinite chain may get saturated to non-zero values after a sufficiently large number of driving cycles. Moreover, we investigate the convergence of local density matrices, from which the quantum correlations under study originate, towards the final steady-state density matrices as a function of driving cycles. We find that the geometric distance, $d$, between the reduced density matrices of non-equilibrium state and steady-state obeys a power-law scaling of the form $d sim n^{-B}$, where $n$ is the number of driving cycles and $B$ is the scaling exponent. The steady-state quantum correlations are studied as a function of time period of the driving field and are marked by the presence of prominent peaks in frequency domain. The steady-state features can be further understood by probing band structures of Floquet Hamiltonian and purity of the bipartite state between nearest neighbor sites. Finally, we compare the steady-state values of the local quantum correlations with that of the canonical Gibbs ensemble and infer about their canonical ergodic properties. Moreover, we identify generic features in the ergodic properties depending upon the quantum phases of the initial state and the pathway of repeated driving that may be within the same quantum phase or across two different equilibrium phases.
We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realised in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.
For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several truncations of the time evolution equations up to eighth order in the Jordan-Wigner fermionic operators. The resulting set of differential equations can be solved for lattices with $O(10^2)$ sites and facilitates the computation of spin expectation values and correlation functions to high accuracy, at least for moderate timescales. We use this scheme to study the relaxation dynamics of the model, involving prethermalisation and thermalisation. The techniques developed here can be generalised to other spin models with weak integrability-breaking terms.
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