arXiv subjects

R. Jafari

Publications and source records attributed to R. Jafari.

At least 55 records · Page 3Linked to original sources

arXiv2017

Magnetic quantum correlation in the 1D transverse-field XXZ model

One-dimensional spin-1/2 systems are well-known candidates to study the quantum correlations between particles. In the condensed matter physics, studies often are restricted to the 1st neighbor particles. In this work, we consider the 1D XXZ model in a transverse magnetic field (TF) which is not integrable except at specific points. Analytical expressions for quantum correlations (entanglement and quantum discord) between spin pairs at any distance are obtained for both zero and finite temperature, using an analytical approach proposed by Caux et al. [PRB 68, 134431 (2003)]. We compare the efficiency of the QD with respect to the entanglement in the detection of critical points (CPs) as the neighboring spin pairs go farther than the next nearest neighbors. In the absence of the TF and at zero temperature, we show that the QD for spin pairs farther than the 2nd neighbors is able to capture the critical points while the pairwise entanglement is absent. In contrast to the pairwise entanglement, two-site quantum discord is effectively long-range in the critical regimes where it decays algebraically with the distance between pairs. We also show that the thermal quantum discord between neighbor spins possesses strong distinctive behavior at the critical point that can be seen at finite temperature and, therefore, spotlights the critical point while the entanglement fails in this task.

cond-mat.str-el↗

arXiv2017

Loschmidt Echo Revivals: Critical and Noncritical

A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point $-$ measuring the time dependence of the overlap between initial and time-evolved states $-$ is expected to exhibit an accelerated relaxation followed by periodic revivals. We here introduce a new exactly solvable model, the extended Su-Schrieffer-Heeger model, the Loschmidt echo of which provides a counterexample. A parallell analysis of the quench dynamics of the three-site spin-interacting $XY$ model allows us to pinpoint the conditions under which a periodic Loschmidt revival actually appears

quant-ph↗

arXiv2017

Real space renormalization of Majorana fermions in quantum nano-wire superconductors

We have applied the real space quantum renormalization group approach to study the topological quantum phase transition in the one-dimensional chain of a spinless p-wave superconductor. We investigate the behavior of local compressibility and ground-state fidelity of the Kitaev chain. We show that the topological phase transition is signaled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point have been used as a proper indicators for the topological quantum phase transition, which signals the appearance of Majorana fermions. We also present the scaling analysis of ground-state fidelity near the critical point that manifests the universal information about the topological phase transition.

cond-mat.supr-con↗

arXiv2015

Gapped Quantum Criticality Gains Long Time Quantum Correlations

We show gapped critical environment could remarkably prevent an enhanced decay of decoherence factor and quantum correlations at the critical point, which is nontrivially different from the ones in a gapless critical environment (Quan, et.al Phys. Rev. Lett. \textbf{96}, 140604 (2006)). The quantum correlations display very fast decaying to their local minimum at the critical point while maximum decaying occurs away from this point. In particular, our results imply that collapse of decoherence factor is not indicator of a quantum phase transition of environment as opposed to what happens in a gapless criticallity. In the week coupling regime, the relaxation time, at which the quantum correlations touch rapidly local minima, shows a power-law singularity as a function of gap. Furthermore, quantum correlations decay exponentially with second power of relaxation time. Our results are important for a better understanding and characterisation of gap critical environment and its ability as entanglers in open quantum systems.

quant-ph↗

arXiv2015

Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

We study the ground state fidelity, fidelity susceptibility and quench dynamics of the extended quantum compass model in a transverse field. This model reveals a rich phase diagram which includes several critical surfaces depending on exchange couplings. We present a characterization of quantum phase transitions in terms of the ground state fidelity between two ground states obtained for two different values of external parameters. However, we derive scaling relations describing the singular behavior of fidelity susceptibility in the quantum critical surfaces. Moreover, we study the time evolution of the system after a critical quantum quench using the Loschmidt. We find that the revival times of Loschmidt echo are given by $T_{rev}=N/2v_{max}$, where $N$ is the size of the system and $v_{max}$ is the maximum of lower bound group velocity of quasi-particles. Although the fidelity susceptibility shows the same exponent in all critical surfaces, the structure of the revivals after critical quantum quenches displays two different regimes reflecting different equilibration dynamics.

cond-mat.stat-mech↗

arXiv2014

Induced effects of the Dzyaloshinskii-Moriya interaction on the thermal entanglement in spin-1/2 Heisenberg chains

The nearest neighbor spins in the one-dimensional (1D) spin-1/2 XX model with 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 $h_c$. Using the fermionization technique, we have studied the mutual effect of the DM interaction and TF on the thermal entanglement (TE) in this model. The critical temperature, where the entanglement disappears is specified. It is found that the TE at a finite temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argued 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.

cond-mat.str-el↗

arXiv2014

Geometric Phase and Fidelity of The One-Dimensional Extended Quantum Compass Model in a Transverse Field

We study the geometric phase of the ground state in the extended quantum compass model in presence of a transverse field. The exact solution is obtained by using the Jordan-Wigner transformation which maps the Hamiltonian on a fermionic system and applying the Fourier transformation to realize the diagonalization and an analytical expression for the ground state and geometric phase in the momentum space. Furthermore, the scaling behavior of the extremum of geometric phase and its universality are investigated due to the divergence of geometric phase at the critical point.

cond-mat.str-el↗

arXiv2014

Topological Phase Transition in the Extended Cluster Compass Ladder

We have studied the exact solution of the extended cluster compass ladder, which is equivalent to extended quantum compass model with cluster interaction between next-nearest-neighbor spins, by using the Jordan-Wigner transformation. We show that this model is always gapfull except at the critical surfaces where the energy gap disappears. We obtain the analytic expressions of all critical couplings which drive quantum phase transitions. This model shows a rich phase diagram which includes spin-flop, strip antiferromagnetic and topological ordered on the legs, in addition to the phase with antiparallel ordering of spin y component on the rungs. We study also the universality and scaling properties of the three point correlation functions derivatives in different regions to confirm the results obtained using the energy gap analysis. On the other hand, we have replaced the cluster interaction with usual form and using the Lanczos method a numerical experiment is done. Analyzing the numerical results, we show that the effect of the cluster interaction between next-nearest-neighbor spins is completely different from the usual form.

cond-mat.str-el↗

arXiv2013

Quantum renormalization group approach to geometric phases in spin chains

A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative and its position scales with an exponent of the system size. This exponent is directly associated with the critical properties of the model where, the exponent governing the divergence of the correlation length close to the quantum critical point.

cond-mat.str-el↗

arXiv2011

Thermodynamic Properties of the One-Dimensional Extended Quantum Compass Model in the Presence of a Transverse Field

The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T; c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect.

cond-mat.str-el↗

arXiv2011

Universality and Scaling Properties of Correlation Functions Near a Quantum Phase Transition

In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of correlation functions with respect to the parameter that drives the quantum phase transitions, exhibit logarithmic divergence and finite size scaling the same as entanglement. In other words the non-analytic and finite size scaling behaviors of entanglement is not its intrinsic properties and inherit from the non-analytic and scaling behaviors of correlation functions and surveying at least the nearest neighbor correlation functions could specify the scaling and divergence properties of entanglement. However we show that the correlation functions could capture the quantum critical point without pre-assumed order parameters even for the cases where the two-body entanglement is absent.

cond-mat.str-el↗

arXiv2011

Quantum Phase Transition in the One-Dimensional Extended Quantum Compass Model in a Transverse Field

Quantum phase transitions in the one-dimensional extended quantum compass model in transverse field are studied by using the Jordan-Wigner transformation. This model is always gapful except at the critical surfaces where the energy gap disappears. We obtain the analytic expressions of all critical fields which drive quantum phase transitions. This model shows a rich phase diagram which includes spin-flop, strip antiferromagnetic and saturate ferromagnetic phases in addition to the phase with anti parallel ordering of spin $y$ component on odd bonds. However we study the universality and scaling properties of the transverse susceptibility and nearest-neighbor correlation functions derivatives in different regions to confirm the results obtained using the energy gap analysis.

cond-mat.str-el↗

arXiv2010

Low energy states dynamic of entanglement for spin systems

We have composed the ideas of quantum renormalization group and quantum information by exploring the low energy states dynamic of entanglement resources of a system close to its quantum critical point. We demonstrate the low energy states dynamical quantities of the one dimensional magnetic systems could show the quantum phase transition point and shows the scaling behavior in the vicinity of the transition point. To present our idea, we study the evolution of two spins entanglement in the one-dimensional Ising model in the transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We investigate evolvement of the generation of entanglement with increasing the magnetic field. We have obtained that the derivative of the time at which the entanglement reaches its maximums with respect to the transverse field, diverges at the critical point and its scaling behaviors versus the size of the system are as same as the static ground state entanglement of the the system.

quant-ph↗

arXiv2009

Dzyaloshinskii-Moriya Interaction and Anisotropy effects on the Entanglement of Heisenberg Model

In this paper the the effect of Dzyaloshinskii-Moriya interaction and anisotropy on the Entanglement of Heisenberg chain has been studied. While the anisotropy suppress the entanglement due to favoring of the alignment of spins, the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations. Thermodynamic limit of the model and emerging of non-analytic behavior of the entanglement have also been probed. The singularities of the entanglement correspond to the critical boundary separating different phases of the model. The singularity of the entanglement derivative approaches the critical point from the gapped phase and will be symmetric if both phase on the boundary are gapped.

quant-ph↗

arXiv2009

Three-Qubit Ground State and Thermal Entanglement of $XXZ$ Model With Dzyaloshinskii-Moriya Interaction

We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubit anisotropic Heisenberg (XXZ) and Ising in a magnetic field models and in the presence of Dzyaloshinskii-Moriya (DM) interaction. We have found that increasing of the DM interaction and magnetic field can enhance and reduce the entanglement of system. We have shown that the non-symmetric pairwise has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise. For negative anisotropy the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in details. The most remarkable result happens at zero temperature where 3-qubit ground state entanglement of the system (in spite of 2-qubit counterpart) shows the fingerprint of quantum phase transition for an infinite size system.

quant-ph↗

arXiv2008

Phase Diagram of spin 1/2 XXZ Model With Dzyaloshinskii-Moriya Interaction

We have studied the phase diagram of the one dimensional XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has three phases, ferromagnetic, spin-fluid and Néel phases which are separated by a critical line which depends on the DM coupling constant. We have shown that the staggered magnetization is the order parameter of the system and investigated the influence of DM interaction on the chiral ordering as a helical magnetic order.

cond-mat.str-el↗

arXiv2008

Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction

We have studied the phase diagram and entanglement of the one dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has two phases, antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of new spin operators which are defined by a nonlocal transformation.

cond-mat.str-el↗

arXiv2008

The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model

We have applied our recent approach (Kargarian, et.al Phys. Rev. A 76, 60304 (R) (2007)) to study the quantum information properties of the anisotropic s=1/2 Heisenberg chain. We have investigated the underlying quantum information properties like the evolution of concurrence, entanglement entropy, nonanalytic behaviours and the scaling close to the quantum critical point of the model. Both the concurrence and the entanglement entropy develop two saturated values after enough iterations of the renormalization of coupling constants. This values are associated with the two different phases, i.e Neel and spin liquid phases. The nonanalytic behaviour comes from the divergence of the first derivative of both measures of entanglement as the size of system becomes large. The renormalization scheme demonstrates how the minimum value of the first derivative and its position scales with an exponent of the system size. It is shown that this exponent is directly related to the critical properties of the model, i.e. the exponent governing the divergence of the correlation length close to the quantum critical point. We also use a renormalization method based on the quantum group concept in order to get more insight about the critical properties of the model and the renormalization of entanglement.

quant-ph↗