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arXiv:1806.02125 · Physical review. B./Physical review. B

Photoinduced entanglement in a magnonic Floquet topological insulator

Satyaki Kar, Banasri Basu

Published Dec 13, 2018• 17 citations
arXivHTMLPDF

Abstract

When irradiated via high-frequency circularly polarized light, the stroboscopic dynamics in a Heisenberg spin system on a honeycomb lattice develops a next-nearest-neighbor (NNN) Dzyaloshinskii-Moriya (DM) type term, making it a magnonic Floquet topological insulator. We investigate the entanglement generation and its evolution on such systems, particularly an irradiated ferromagnetic XXZ spin-$\frac{1}{2}$ model in a honeycomb lattice as the system parameters are optically tuned. In the high-frequency limit, we compute the lowest quasienergy state entanglement in terms of the concurrence between nearest-neighbor (NN) and NNN pair of spins and witness the entanglement transitions occurring there. For the easy-axis scenario, the unirradiated system forms a product state but entanglement grows between the NNN spin pairs beyond some cutoff DM strength. Contrarily in the easy-planar case, NN and NNN spins remain already entangled in the unirradiated limit. It then goes through an entanglement transition which causes decrease (increase) of the NN (NNN) concurrences down to zero (up to some higher value) at some critical finite DM interaction strength. For a high frequency of irradiation and a suitably chosen anisotropy parameter, we can vary the field strength to witness sudden death and revival of entanglement in the Floquet system. Both exact diagonalization and modified Lanczos techniques are used to obtain the results up to 24 site lattice. We also calculate the thermal entanglement and obtain estimates for the threshold temperatures below which nonzero concurrence can be expected in the system.

DOI
10.1103/physrevb.98.245119

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When irradiated via high-frequency circularly polarized light, the stroboscopic dynamics in a Heisenberg spin system on a honeycomb lattice develops a next-nearest-neighbor (NNN) Dzyaloshinskii-Moriya (DM) type term, making it a magnonic Floquet topological insulator. We investigate the entanglement generation and its evolution on such systems, particularly an irradiated ferromagnetic XXZ spin-12\frac{1}{2}21​ model in a honeycomb lattice as the system parameters are optically tuned. In the high-frequency limit, we compute the lowest quasienergy state entanglement in terms of the concurrence between nearest-neighbor (NN) and NNN pair of spins and witness the entanglement transitions occurring there. For the easy-axis scenario, the unirradiated system forms a product state but entanglement grows between the NNN spin pairs beyond some cutoff DM strength. Contrarily in the easy-planar case, NN and NNN spins remain already entangled in the unirradiated limit. It then goes through an entanglement transition which causes decrease (increase) of the NN (NNN) concurrences down to zero (up to some higher value) at some critical finite DM interaction strength. For a high frequency of irradiation and a suitably chosen anisotropy parameter, we can vary the field strength to witness sudden death and revival of entanglement in the Floquet system. Both exact diagonalization and modified Lanczos techniques are used to obtain the results up to 24 site lattice. We also calculate the thermal entanglement and obtain estimates for the threshold temperatures below which nonzero concurrence can be expected in the system.
Dynamics of the nearest-neighbor concurrence and the block–block entanglement in closed Heisenberg chains with Dzyaloshinskii–Moriya (DM) interactions are simulated numerically. It is found that the nearest-neighbor concurrence and the block–block entanglement can be generated dynamically from an initial antiferromagnetic (AF) state, and DM interactions will enhance the amplitude of oscillation of concurrence and that of block–block entanglement. Furthermore, dynamics of block–block entanglement SL in the chain with even number spins is coincident with the dynamics of SN - L for D = 0. However, with the consideration of DM interactions, the evolution of SL will not be consistent with that of SN - L for the chain with odd number spins. In a given time interval, the maximal value of the generated nearest-neighbor concurrence [Formula: see text] will first decrease with the increase of chain's length, then oscillate with the increase of N. The maximal value and the minimal value of the oscillation becomes stable for a large N, and [Formula: see text] of the chain with odd spins is larger than that of the chain with even spins for a large N. The influence of DM interaction on the value of [Formula: see text] becomes unobvious with the increase of chain's length.
The phenomenon of quantum entanglement has a very important role in quantum mechanics. Particularly, the quantum spin chain provides a platform for theoretical and experimental investigation of many-body entanglement. In this paper, we investigate time evolution of entanglement in a four-qubit anisotropic Heisenberg XXZ chain with nearest neighboring (NN), the next nearest neighboring (NNN), and the Dzialoshinskii-Moriya (DM) interactions. Calculations of the entanglement evolution of the Werner state carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, frustration, etc. The results show that for the Werner state, DM interaction and the frustration parameters play important roles. Furthermore, results show that the time evolution of the Werner state entanglement may be useful to capture the quantum phase transitions in quantum magnetic systems.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
The nearest-neighbor spins in the one-dimensional spin-1/2 XXXXXX model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field, hc{h}_{c}hc​. Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.
One of the challenges in quantum information is to create quantum states that can be used as resources, for instance, in the measurement-based model of quantum computing. Here, the author investigates the generation, through a dynamical phase transition, of a topological entangled state, by the Floquet evolution of a chain of spins, whose ground state is the so-called cluster state, acted upon by a quantum walker. The nonergodic phase is characterized by the emergence of magnetic order, persistent at long times.