Quantum phase transitions about parity breaking in matrix product systems

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.     

Quantum phase transitions about parity breaking in matrix product systems

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.     

Quantum phase transitions in matrix product systems

We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of "conventional" QPTs.     

Properties of Parity Non-conserved and Parity Conserved States in MatrixProduct Systems

In terms of reflection transformation of a matrix product state (MPS), the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Ψ_e> and the odd-parity state |Ψ_o>. It is interesting to find that the parity non-conserved reflective MPSpair have no long-range correlations; instead the even-parity state|Ψ_e> and the odd-parity state |Ψ_o> constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Ψ_e> and |Ψ_o > is larger than that for the reflective MPS pair except for n=1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. Thesecharacteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.     

Quantum Phase Transitions in Conventional Matrix Product Systems

For matrix product states(MPSs) of one-dimensional spin-\(\frac {1}{2}\) chains, we investigate a new kind of conventional quantum phase transition(QPT). We find that the system has two different ferromagnetic phases; on the line of the two ferromagnetic phases coexisting equally, the system in the thermodynamic limit is in an isolated mediate-coupling state described by a paramagnetic state and is in the same state as the renormalization group fixed point state, the expectation values of the physical quantities are discontinuous, and any two spin blocks of the system have the same geometry quantum discord(GQD) within the range of open interval (0,0.25) and the same classical correlation(CC) within the range of open interval (0,0.75) compared to any phase having no any kind of correlation. We not only realize the control of QPTs but also realize the control of quantum correlation of quantum many-body systems on the critical line by adjusting the environment parameters, which may have potential application in quantum information fields and is helpful to comprehensively and deeply understand the quantum correlation, and the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems.     

No Spin-Localization Phase Transition in the Spin-Boson Model without Local Field

We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition （QPT） happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. The parity breaking mentioned in our case is completely different from the spontaneously broken symmetry relevant to the conventionally defined QPT in previous studies. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no- degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to incorrect employment of the ground state of the model and/or unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.     

No Spin-Localization Phase Transition in the Spin-Boson Model without Local Field

We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. The parity breaking mentioned in our case is completely different from the spontaneously broken symmetry relevant to the conventionally defined QPT in previous studies. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no-degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to incorrect employment of the ground state of the model and/or unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.     

Entanglement, quantum phase transition and fixed-point bifurcation in the N-atom Jaynes-Cummings model with an additional symmetry breaking term

In the present work we analyze the quantum phase transition (QPT) in the N-atom Jaynes-Cummings model (NJCM) with an additional symmetry breaking interaction term in the Hamiltonian. We show that depending on the type of symmetry breaking term added the transition order can change or not and also the fixed point associated to the classical analogue of the Hamiltonian can bifurcate or not. We present two examples of symmetry broken Hamiltonians and discuss based on them, the interconnection between the transition order, appearance of bifurcation and the behavior of the entanglement.     

Quantum Phase Transitions,Entanglement Spectrum,and Schmidt Gap in Bond-Alternative S=1 Antiferromagnetic Chain

Bipartite entanglement, entanglement spectrum, and Schmidt gap in S=1 bond-alternative antiferromagnetic Heisenberg chain are investigated by the infinite time-evolving block decimation （iTEBD） method. The quantum phase transition （QPT） from the singlet-dimer phase to the Haldane phase can be detected by the singular behavior of bipartite entanglement, the sudden change of the entanglement spectrum, and the completely vanishing of the Schmidt gap. The critical point is determined to be around rc ~- 0.587, and the second-order character of the QPT is verified. Doubly degenerate entanglement spectra of both even and odd bonds are observed in the Haldane phase, by which one can distinguish the Haldane phase from the singlet-dimer phase easily. Nearest-neighbor antiferromagnetic correlations and next-nearest-neighbor ferromagnetic correlations are found in the whole parameter region. At the critical massless point, although exponentially decaying antiferromagnetie correlation is observed, it approaches to a constant value finally. Therefore, long-range correlations exist and the correlation length becomes divergent at the critical point.     

Multipartite entanglement signature of quantum phase transitions

We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.     

Two mode photon bunching effect as witness of quantum criticality in circuit QED

We suggest a scheme to probe critical phenomena at a quantum phase transition (QPT) using the quantum correlation of two photonic modes simultaneously coupled to a critical system. As an experimentally accessible physical implementation, a circuit QED system is formed by a capacitively coupled Josephson junction qubit array interacting with one superconducting transmission line resonator (TLR). It realizes an Ising chain in the transverse field (ICTF) which interacts with the two magnetic modes propagating in the TLR. We demonstrate that in the vicinity of criticality the originally independent fields tend to display photon bunching effects due to their interaction with the ICTF. Thus, the occurrence of the QPT is reflected by the quantum characteristics of the photonic fields.     

Coherence and Quantum Phase Transition in Spin Models

Based on quantum renormalization group (QRG) method, we investigated quantum coherence and quantum phase transition (QPT) in XXZ chain and XY chain, respectively. The results show that both the geometric quantum coherence and entropic coherecne can accurately indicate the QPT at critical point after enough iteration steps. Moreover, the increasing anisotropy parameter destroys the coherence in the XXZ chain, while enhances it in the XY chain. In addition, focused on the XXZ chain we analyzed the nonanalytic phenomena and scaling behaviors with different theoretical exponents in detail.

     

Critical entanglement and geometric phase of a two-qubitmodel with Dzyaloshinski--Moriya anisotropic interaction

We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski--Moriya (DM) anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition (QPT). It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.     

Entanglement property in matrix product spin systems

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy Sn of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.     

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method. The bond-alternative effects on its ground-state phase diagram are discussed in detail. Once the bond alternation is taken into account, the antiferromagnetic phase (Δ > 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order. The QPT is shown to be second-order, and the whole phase diagram is provided. For the ferromagnetic phase region (Δ < -1), the critical point r^c always equals 1 (independent of Δ), and the QPT for this case is shown to be first-order. The dimerized Heisenberg model is also discussed, and two disordered phases can be distinguished by with or without nonlocal string orders. Both the bipartite entanglement and the fidelity per site, as two kinds of model-independent measures, are capable of describing all the QPTs in such a quantum model.     

Quantum phase transition and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a double-well potential

We investigate the quantum phase transition (QPT) and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a symmetric double well under the mean-field approximation. We find the system undergoes a new QPT towards phase-locking state when atom-pair tunnelling is strong enough, and the critical point of self-trapping QPT is shifted by atom-pair tunnelling. As for the dynamics, the system displays localized dynamical behaviour: phase-locking motion and self-trapping motion. We further study the correlation between this localized dynamics and QPT, and find that the area of the localized trajectories in the phase space can serve as an order parameter for both QPTs. The critical exponent of this order parameter is also discussed.     

Negativity and Quantum Phase Transition in the Spin Model Using the Quantum Renormalization-group Method

In this paper, we study the anisotropy parameter and Dzyaloshinskii-Moriya (DM) interaction on negativity and quantum phase transition (QPT) by using the quantum renormalization-group (QRG) method in the spin model. In our model, the anisotropy parameter and DM interaction can influence the phase diagrams. Negativity can develop two different values which separated two phases i.e. Spin-fluid phase and the Néel phase with the number of QRG iterations increased, and can obviously exhibit QPT at the critical point. Then, we find that negativity of particles 1, 3 throughout is less than negativity of particles 1, 2 or particles 2, 3. Because of information between the three particle distributions, please see the conclusion. We find that the negativity difference value (S) can also clearly detect QPT at the critical point. Most importantly, the maximum S _max become more and more close to the critical point. So S _max can be used as a criterion of the quantum phase transition occurrence when the spin chain is infinity (N → ∞).     

Robust tori-like Lagrangian coherent structures

In general the term “Lagrangian coherent structure” (LCS) is used to make reference about structures whose properties are similar to a time-dependent analog of stable and unstable manifolds from a hyperbolic fixed point in Hamiltonian systems. Recently, the term LCS was used to describe a different type of structure, whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. A new kind of LCS was obtained. It consists of barriers, called robust tori that block the trajectories in certain regions of the phase space. We used the Double-Gyre Flow system as the model. In this system, the robust tori play the role of a skeleton for the dynamics and block, horizontally, vortices that come from different parts of the phase space.     

Quantum Phase Transition and Thermal Entanglement in the Isotropic XXX Model

We investigate the quantum phase transition (QPT) and the pairwise thermal entanglement in the three-qubit Heisenberg XXX chain with Dzyaloshinskii--Moriya (DM) interaction under a magnetic field. The ground states of the system exist crossing points, which shows that the system exhibits a QPT. At a given temperature, the entanglement undergoes two sudden changes (platform-like behavior) as the DM interaction or external magnetic field increases. This special property can be used as the entanglement switch, which is also influenced by the temperature. We can modulate the DM interaction or external magnetic field to control the entanglement switch.