Entanglement transition in a cluster spin chain coupled with free spins

We investigate the entanglement of a ladder of spins formed by two sublattices, a “cluster” chain and the “environment”, consisting of independent spins, both coupled by an exchange interaction and evolving under a unitary discrete-time dynamics. The automaton is defined by the composition of the two-body spin-swap gate (between sublattices) and the three-body cluster interaction. We observe that, depending on the set of coupling constants, the cluster subsystem evolves towards states corresponding to different entanglement phases. In the weak-coupling regime the subsystem remains near the topological cluster state. Increasing the coupling strength leads to random states that transform from almost pure to fully mixed, according to the effective number of the environment's active degrees of freedom.We investigate the entanglement of a ladder of spins formed by two sublattices, a “cluster” chain and the “environment”, consisting of independent spins, both coupled by an exchange interaction and evolving under a unitary discrete-time dynamics. The automaton is defined by the composition of the two-body spin-swap gate (between sublattices) and the three-body cluster interaction. We observe that, depending on the set of coupling constants, the cluster subsystem evolves towards states corresponding to different entanglement phases. In the weak-coupling regime the subsystem remains near the topological cluster state. Increasing the coupling strength leads to random states that transform from almost pure to fully mixed, according to the effective number of the environment's active degrees of freedom.

arXiv:2501.05937Physical review. B./Physical review. BAug 13, 20250 citations

Ground-state entanglement in a system with many-body interactions

Xinhua Peng, Jingfu Zhang, Jiangfeng Du +1 more

Entanglement refers to the inability of many-body quantum mechanical systems to be separated into independent subsystems. This has been well investigated in systems consisting of two entangled subsystems. In larger systems, more complex types of entanglement exist. In a system consisting of three subsystems (e.g., qubits), it is possible that all three subsystems are entangled with each other in a way that cannot be reduced to bipartite entanglement, and it is known that two different, inequivalent forms of tripartite entanglement exist such as the GHZ and $W$ states (GHZ denotes ``Greenberger-Horne-Zeilinger''). Here, we investigate a particularly interesting system with competing one-, two-, and three-body interactions. Its ground state can be a product state, a GHZ state, or a $W$ state, depending on the type and strength of the spin-spin couplings. By varying an external control parameter, the system can be made to undergo quantum transitions between the various ground-state-entanglement phases. We implement the system in an NMR quantum simulator and use adiabatic evolution of the effective Hamiltonian to drive the system through the quantum transitions. In the experimental and numerical simulations, we check the suitability of different observables for making the quantum transitions visible and for characterizing the different phases.Entanglement refers to the inability of many-body quantum mechanical systems to be separated into independent subsystems. This has been well investigated in systems consisting of two entangled subsystems. In larger systems, more complex types of entanglement exist. In a system consisting of three subsystems (e.g., qubits), it is possible that all three subsystems are entangled with each other in a way that cannot be reduced to bipartite entanglement, and it is known that two different, inequivalent forms of tripartite entanglement exist such as the GHZ and $W$ states (GHZ denotes ``Greenberger-Horne-Zeilinger''). Here, we investigate a particularly interesting system with competing one-, two-, and three-body interactions. Its ground state can be a product state, a GHZ state, or a $W$ state, depending on the type and strength of the spin-spin couplings. By varying an external control parameter, the system can be made to undergo quantum transitions between the various ground-state-entanglement phases. We implement the system in an NMR quantum simulator and use adiabatic evolution of the effective Hamiltonian to drive the system through the quantum transitions. In the experimental and numerical simulations, we check the suitability of different observables for making the quantum transitions visible and for characterizing the different phases.

Physical Review AApr 27, 201028 citations

Decoherence from a spin-chain with three-site interaction

Li-Jun Tian, Cai-Yun Zhang, Li‐Guo Qin

We investigate the time evolution of quantum discord and entanglement for two-qubit coupled to a spin chain with three-site interaction in the weak-coupling region. If the quantum system evolves from a Bell state, quantum correlations decay to zero in a very short time at the critical point of the environment. We found there exist some special interval of the three-site coupling strength in which the decay of quantum discord and entanglement can be delayed. When the qubits are initially prepared in a Bell diagonal state, the decay of entanglement is also delayed in the special interval, but the decay of quantum discord is enhanced. Besides, the sudden transition between classical and quantum decoherence is observed. we found the transition time can be lengthened at the special range of three-site interaction and shorten by degree of anisotropy.We investigate the time evolution of quantum discord and entanglement for two-qubit coupled to a spin chain with three-site interaction in the weak-coupling region. If the quantum system evolves from a Bell state, quantum correlations decay to zero in a very short time at the critical point of the environment. We found there exist some special interval of the three-site coupling strength in which the decay of quantum discord and entanglement can be delayed. When the qubits are initially prepared in a Bell diagonal state, the decay of entanglement is also delayed in the special interval, but the decay of quantum discord is enhanced. Besides, the sudden transition between classical and quantum decoherence is observed. we found the transition time can be lengthened at the special range of three-site interaction and shorten by degree of anisotropy.

arXiv:1210.5004Oct 18, 20120 citations

Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system

Alessio Mauro Franchi, Andrea Pelissetto C, Ettore Vicari

We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part E, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem S under scrutiny, and the other one with the environment E. We investigate the behavior of S at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a quench of the coupling between S and E. When S develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of E, whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of E, are observed for the decoherence of the subsystem S, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with E.We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part E, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem S under scrutiny, and the other one with the environment E. We investigate the behavior of S at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a quench of the coupling between S and E. When S develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of E, whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of E, are observed for the decoherence of the subsystem S, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with E.

arXiv:2209.06523Physical review. EJan 13, 20232 citations

Non-Markovian dynamics in the extended cluster spin-1/2 XX chain

Maryam Mahmoudi, S. Mahdavifar, T. Mohammad Ali Zadeh +1 more

We study the dynamics of entanglement, mutual information, and quantum discord in the extended cluster spin-1/2 $\mathit{XX}$ chain, equivalent to a one-dimensional spin-1/2 $\mathit{XX}$ model with three-spin interaction (TSI). Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the environment. The two-point Heisenberg and the TSI are responsible for coupling between the system and the environment. Although the revival phenomenon of quantum correlations as an indication of non-Markovian dynamics is observed for TSI stronger than the Heisenberg interaction, the study of the trace distance has proven that the dynamical phase transition from the Markovian to the non-Markovian regime happens at a critical value where the TSI is equal to half of the Heisenberg interaction. By focusing on the nearest neighbor pair spins of the environment, we have also shown that the dynamics of quantum correlation in the environment is sensitive to Markovian and non-Markovian regions.We study the dynamics of entanglement, mutual information, and quantum discord in the extended cluster spin-1/2 $\mathit{XX}$ chain, equivalent to a one-dimensional spin-1/2 $\mathit{XX}$ model with three-spin interaction (TSI). Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the environment. The two-point Heisenberg and the TSI are responsible for coupling between the system and the environment. Although the revival phenomenon of quantum correlations as an indication of non-Markovian dynamics is observed for TSI stronger than the Heisenberg interaction, the study of the trace distance has proven that the dynamical phase transition from the Markovian to the non-Markovian regime happens at a critical value where the TSI is equal to half of the Heisenberg interaction. By focusing on the nearest neighbor pair spins of the environment, we have also shown that the dynamics of quantum correlation in the environment is sensitive to Markovian and non-Markovian regions.

arXiv:1607.02837Physical Review AJan 30, 201716 citations

Decoherence of Bell states by local interactions with a dynamic spin environment

Cecilia Cormick, Juan Pablo Paz

We study the evolution of a system of two qubits, each of which interacts locally with a spin chain with nontrivial internal Hamiltonian. We present an exact solution to this problem and analyze the dependence of decoherence on the distance between the interaction sites. In the strong coupling regime we find that decoherence increases with increasing distance. In the weak coupling regime the dependence of decoherence with distance is not generic (i.e., it varies according to the initial state). Decoherence becomes independent of distance when the latter is over a saturation length $l$ . Numerical results for the Ising chain suggest that the saturation scale is related to the correlation length $\ensuremath{\xi}$. For strong coupling we display evidence of the existence of non-Markovian effects (such as environment-induced interactions between the qubits). As a consequence the system can undergo a quasiperiodic sequence of ``sudden deaths and revivals'' of entanglement, with a time scale related to the distance between qubits.We study the evolution of a system of two qubits, each of which interacts locally with a spin chain with nontrivial internal Hamiltonian. We present an exact solution to this problem and analyze the dependence of decoherence on the distance between the interaction sites. In the strong coupling regime we find that decoherence increases with increasing distance. In the weak coupling regime the dependence of decoherence with distance is not generic (i.e., it varies according to the initial state). Decoherence becomes independent of distance when the latter is over a saturation length $l$. Numerical results for the Ising chain suggest that the saturation scale is related to the correlation length $\ensuremath{\xi}$. For strong coupling we display evidence of the existence of non-Markovian effects (such as environment-induced interactions between the qubits). As a consequence the system can undergo a quasiperiodic sequence of ``sudden deaths and revivals'' of entanglement, with a time scale related to the distance between qubits.

arXiv:0804.0241Physical Review AJul 29, 200826 citations

W

states (GHZ denotes ``Greenberger-Horne-Zeilinger''). Here, we investigate a particularly interesting system with competing one-, two-, and three-body interactions. Its ground state can be a product state, a GHZ state, or a

W

state, depending on the type and strength of the spin-spin couplings. By varying an external control parameter, the system can be made to undergo quantum transitions between the various ground-state-entanglement phases. We implement the system in an NMR quantum simulator and use adiabatic evolution of the effective Hamiltonian to drive the system through the quantum transitions. In the experimental and numerical simulations, we check the suitability of different observables for making the quantum transitions visible and for characterizing the different phases.

We study the dynamics of entanglement, mutual information, and quantum discord in the extended cluster spin-1/2

\mathit{XX}

chain, equivalent to a one-dimensional spin-1/2

\mathit{XX}

model with three-spin interaction (TSI). Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the environment. The two-point Heisenberg and the TSI are responsible for coupling between the system and the environment. Although the revival phenomenon of quantum correlations as an indication of non-Markovian dynamics is observed for TSI stronger than the Heisenberg interaction, the study of the trace distance has proven that the dynamical phase transition from the Markovian to the non-Markovian regime happens at a critical value where the TSI is equal to half of the Heisenberg interaction. By focusing on the nearest neighbor pair spins of the environment, we have also shown that the dynamics of quantum correlation in the environment is sensitive to Markovian and non-Markovian regions.

l

. Numerical results for the Ising chain suggest that the saturation scale is related to the correlation length $\ensuremath{\xi}$. For strong coupling we display evidence of the existence of non-Markovian effects (such as environment-induced interactions between the qubits). As a consequence the system can undergo a quasiperiodic sequence of ``sudden deaths and revivals'' of entanglement, with a time scale related to the distance between qubits.