We study the decoherence of a spin-1/2 induced by an environment which is on the verge of a continuous phase transition. We consider spin environments described by the ferromagnetic and antiferromagnetic Heisenberg models on a square lattice. As is well known, these two-dimensional systems undergo a continuous phase transition at zero temperature, where the spins order spontaneously. For weak coupling of the central spin to these baths, we find that as one approaches the transition temperature, critical fluctuations make the central spin decohere faster. Furthermore, the decoherence is maximal at zero temperature as signaled by the divergence of the Markovian decoherence rate.We study the decoherence of a spin-1/2 induced by an environment which is on the verge of a continuous phase transition. We consider spin environments described by the ferromagnetic and antiferromagnetic Heisenberg models on a square lattice. As is well known, these two-dimensional systems undergo a continuous phase transition at zero temperature, where the spins order spontaneously. For weak coupling of the central spin to these baths, we find that as one approaches the transition temperature, critical fluctuations make the central spin decohere faster. Furthermore, the decoherence is maximal at zero temperature as signaled by the divergence of the Markovian decoherence rate.

Physical Review LettersDec 27, 200710 citations

Quantum phase transition in the four-spin exchange antiferromagnet

Valeri N. Kotov, Dao‐Xin Yao, A. H. Castro Neto +1 more

We study the $S=1/2$ Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.We study the $S=1/2$ Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.

arXiv:0704.0114Physical Review BNov 10, 200917 citations

Decoherence induced by interacting quantum spin baths

Davide Rossini, Tommaso Calarco, Vittorio Giovannetti +2 more

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, $XY$ , or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the $XY$ models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, $XY$, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the $XY$ models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.

arXiv:quant-ph/0611242Physical Review AMar 26, 2007199 citations

Effect of random interactions in spin baths on decoherence

S. Camalet, R. Chitra

We study the decoherence of a central spin- $1∕2$ induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferromagnetic and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising bath. We present analytic results for the Ising spin chain bath at arbitrary temperature for different distributions of the intrabath interaction strengths. We find clear evidence of non-Markovian behavior in the low temperature regime. We also consider baths described by Ising models on higher-dimensional lattices. We find that interactions lead to a significant reduction of the decoherence. An important feature of interacting spin baths is the saturation of the asymptotic Markovian decay rate at high temperatures, as opposed to the conventional Ohmic boson bath.We study the decoherence of a central spin-$1∕2$ induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferromagnetic and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising bath. We present analytic results for the Ising spin chain bath at arbitrary temperature for different distributions of the intrabath interaction strengths. We find clear evidence of non-Markovian behavior in the low temperature regime. We also consider baths described by Ising models on higher-dimensional lattices. We find that interactions lead to a significant reduction of the decoherence. An important feature of interacting spin baths is the saturation of the asymptotic Markovian decay rate at high temperatures, as opposed to the conventional Ohmic boson bath.

arXiv:cond-mat/0610874Physical Review BMar 29, 200730 citations

Giant enhancement of quantum decoherence by frustrated environments

S. Yuan, Mikhail I. Katsnelson, Hans A. De Raedt

Decoherence in a system of two antiferromagnetically coupled spins that interact with a spin bath environment is studied. Systems are considered that range from the rotationally invariant to highly anisotropic spin models and have different topologies and values of parameters that are fixed or are allowed to fluctuate randomly. We explore the conditions under which the two-spin system clearly shows an evolution from the initial spin-up-spin-down state towards the maximally entangled singlet state. We demonstrate that frustration and, especially, glassiness of the spin environment strongly enhances the decoherence of the two-spin system.Decoherence in a system of two antiferromagnetically coupled spins that interact with a spin bath environment is studied. Systems are considered that range from the rotationally invariant to highly anisotropic spin models and have different topologies and values of parameters that are fixed or are allowed to fluctuate randomly. We explore the conditions under which the two-spin system clearly shows an evolution from the initial spin-up-spin-down state towards the maximally entangled singlet state. We demonstrate that frustration and, especially, glassiness of the spin environment strongly enhances the decoherence of the two-spin system.

arXiv:quant-ph/0512232Journal of Experimental and Theoretical Physics LettersSep 1, 200618 citations

Influence of an external magnetic field on the decoherence of a central spin coupled to an antiferromagnetic environment

Xiao-Zhong Yuan, Hsi‐Sheng Goan, Ka-Di Zhu

Using the spin wave approximation, we study the decoherence dynamics of a central spin coupled to an antiferromagnetic environment under the application of an external global magnetic field. The external magnetic field affects the decoherence process through its effect on the antiferromagnetic environment. It is shown explicitly that the decoherence factor which displays a Gaussian decay with time depends on the strength of the external magnetic field and the crystal anisotropy field in the antiferromagnetic environment. When the strength of the external magnetic field is increased to the critical field point at which the spin–flop transition (a first-order quantum phase transition) happens in the antiferromagnetic environment, the decoherence of the central spin reaches its highest point. This result is consistent with several recent quantum phase transition witness studies. The influences of the environmental temperature on the decoherence behaviour of the central spin are also investigated.Using the spin wave approximation, we study the decoherence dynamics of a central spin coupled to an antiferromagnetic environment under the application of an external global magnetic field. The external magnetic field affects the decoherence process through its effect on the antiferromagnetic environment. It is shown explicitly that the decoherence factor which displays a Gaussian decay with time depends on the strength of the external magnetic field and the crystal anisotropy field in the antiferromagnetic environment. When the strength of the external magnetic field is increased to the critical field point at which the spin–flop transition (a first-order quantum phase transition) happens in the antiferromagnetic environment, the decoherence of the central spin reaches its highest point. This result is consistent with several recent quantum phase transition witness studies. The influences of the environmental temperature on the decoherence behaviour of the central spin are also investigated.

arXiv:0706.0934New Journal of PhysicsJul 10, 200722 citations

We study the

S=1/2

Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising,

XY

, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the

XY

models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.

We study the decoherence of a central spin-

1∕2

induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferromagnetic and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising bath. We present analytic results for the Ising spin chain bath at arbitrary temperature for different distributions of the intrabath interaction strengths. We find clear evidence of non-Markovian behavior in the low temperature regime. We also consider baths described by Ising models on higher-dimensional lattices. We find that interactions lead to a significant reduction of the decoherence. An important feature of interacting spin baths is the saturation of the asymptotic Markovian decay rate at high temperatures, as opposed to the conventional Ohmic boson bath.