Quantum Phase Transitions in Matrix Product States

We present a new general and much simpler scheme to construct various quantum phase transitions （Q, PTs） in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state （MPS） OPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of Q, PT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.     

Pairwise Entanglement and Quantum Phase Transitions in Spin Systems

We examine several well-known quantum spin models and categorize the behaviour of pairwise entanglement at quantum phase transitions. A unitied picture on the connection between the entanglement and quantum phase transition in spin systems is presented.     

Metric-Space Approach for Distinguishing Quantum Phase Transitions in Spin-Imbalanced Systems

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions, and potentials) than systems that present different physical behaviors. For this reason, metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here, we apply metric space analysis to explore the transitions between the several phases in spin-imbalanced systems. In particular, we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which density matrix renormalization group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.     

Phase Transitions in Layered Systems

We consider the Ising model on \(\mathbb Z\times \mathbb Z\) where on each horizontal line \(\{(x,i), x\in \mathbb Z\}\) , called “layer”, the interaction is given by a ferromagnetic Kac potential with coupling strength \(J_{ \gamma }(x,y)={ \gamma }J({ \gamma }(x-y))\) , where \(J(\cdot )\) is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength \({ \gamma }^{A}\) , where \(A\ge 2\) is fixed, and prove that for any \(\beta \) larger than the mean field critical value there is a phase transition for all \({ \gamma }\) small enough.     

Decoherence and Phase Transitions in Quantum Dynamics

A particle with internal degrees of freedom is in contact with a bath of photons (necessitating a relativistic treatment). The occurrence of decoherence is established and the density matrix is found to be diagonal in momentum space. In the case of non-trivial internal degrees of freedom and selection rules there is a first order phase transition separating those degrees of freedom. Finally, because probability amplitudes become probabilities, Einstein’s proposal that more than one detector could respond to a signal is answered.

     

Density-Functional Fidelity Approach to Quantum Phase Transitions

We propose a new approach to quantum phase transitions in terms of the density-functional fidelity, which measures the similarity between density distributions of two ground states in parameter space. The key feature of the approach is such that the density-functional fidelity can be measured easily in experiments. Both the validity and versatility of the approach are checked by the Lipkin-Meshkov-Glick model and the one-dimensional Hubbard model.     

Continuous Phase Transitions for Dynamical Systems

We study the asymptotic expansion of the topological pressure of one–parameter families of potentials at a point of non-analyticity. The singularity is related qualitatively and quantitatively to non–Gaussian limit laws and to slow decay of correlations with respect to the equilibrium measure.This work was partially supported by NSF grant DMS–0400687.Dedicated to Y. Pesin on the occasion of his 60th birthday     

有限玻色子系统中的激发态量子相变

为了探讨原子核系统中存在激发态量子相变的可能性,在相互作用玻色子模型框架下对有限玻色子系统中的激发态量子相变现象进行唯象分析,特别是针对角动量和有限N效应如何影响U（5）-SU（3）和SU（3）-O（6）过渡区中的激发态量子相变行为进行了系统研究。结果表明,低角动量振动谱中的激发态量子相变特征在现实玻色子数情况下可以很好地保持,但随着角动量增加相变特征逐渐消失。In this work, a phenomenological analysis of the excited-state quantum phase transitions (ESQPTs) in the finite-N boson system has been carried out within the interacting boson model in order to reveal the possibility of finding ESQPTs in nuclear systems. Particularly, the angular momentum and finite-N effects on the ESQPTs in the U(5)-SU(3) and SU(3)-O(6) transitional regions have been systematically investigated. The results indicate that the main features of ESQPTs can be well preserved even at a realistic boson number for small angular momentum but will gradually disappear as the angular momentum increases.     

Quantum Phase Transitions in Anisotropic Spin Ladders with Antiferromagnetic Rungs

We apply perturbation theory to study quantum phase transitions in anisotropic two-leg spin ladders with antiferromagnetic rungs in the strong interchain coupling limit. The energy gap is expanded up to the fourth order in the ratio of the intrachain to interchain couplings. The transition point is determined by examing the disappearance of the energy gap. Present results for the anisotropic ferromagnetic-leg spin ladder are consistent qualitatively with the nonlinear σ-model analysis and in good agreement with the numerical results by the diagonalization method.     

Quantum Phase Transitions and Dimerized Phases in Frustrated Spin Ladder

In this paper, we study the phase diagram of a frustrated spin ladder model by applying the bosonization technique and the density-matrix renormalization-group (DMRG) algorithm. Effect of the intra-chain next-nearest-neighbor (NNN) super-exchange interaction is investigated in detail and the order parameters are calculated to detect the emergence of the dimerized phases. We find that the intra-chain NNN interaction plays a key role in inducing dimerized phases.     

Phase Portraits of Quantum Systems

We formulate a general approach to construct phase portraits of a quantum system in the Fock–Bargmann space. This approach is applied to simple model problems and two-cluster nuclei as well.     

Understanding Quantum Phase Transitions,edited by Lincoln Carr

The concept of the superdeformed shape is first introduced classically as the most stable configuration of a rapidly rotating deformable body and is then applied to nuclei. The shape of nuclei are determined by a competition between the collective energy of the core, to which classical considerations apply quite well, and the quantal energies of the valence nucleons, which may be evaluated by the Nilsson model. The result of this competition is that slowly rotating nuclei can be either oblate or prolate but rapidly rotating nuclei can have a superdeformed prolate shape, with a 2:1 ratio of axes particularly favoured.

The evidence for superdeformation in nuclei is described under four headings. Firstly, some light nuclei are superdeformed in their ground state or in an excited state. Secondly, some nuclei pass through a well defined superdeformed shape on the way to fission. Thirdly, studies of the excitation functions of elastic and inelastic scattering of identical heavy ions provide evidence of a nuclear molecule in a superdeformed shape. Finally, recent analyses of gamma rays from nuclei formed in a very high spin state by a heavy ion collision provide conclusive evidence for superdeformation.     

Dynamic Opalescence upon Phase Transitions and in Inhomogeneous Systems

The temperature isofrequency dependences of Raman intensities are studied in a number of crystals (lithium tantalate, barium sodium niobate, barium titanate, and quartz) in the low-frequency range near the structural phase-transition points. In the case of ferroelectrics, poly- and single-domain single crystals are studied with a stationary electric field applied to the sample. A drastic increase in the intensity of the quasielastic (low-frequency) light scattering is found when approaching the phase-transition point. The studies are carried out for the 90° scattering geometry as well as at angles close to 180° (backscattering geometry). The anomalies of the quasielastic light scattering near the points of phase transition are observed in the latter case. The position of the maximum intensity of the isofrequency dependence on the temperature scale is found to be dependent on the frequency value = ₀ – (₀ and are the frequency of exciting radiation and the frequency to which the monochromator is tuned, respectively). A theory explaining satisfactorily the observed effect of dynamic opalescence near the phase-transition points in crystals is developed. The specific features of light scattering in an inhomogeneous medium as well as the dynamic properties of the model of such a medium in the form of periodically arranged microresonators are studied. Additional vibrational branches (superlattice vibrations) are shown to be formed in such a medium under certain conditions. These branches give rise to a central peak and strongly affect the characteristics of the structural phase transition depending on the microresonator dimensions. The observing conditions of the dynamic opalescence in inhomogeneous media by the isochronous spectroscopy technique upon pulsed laser excitation are analyzed.     

Quantum Correlation Properties in Composite Parity-Conserved Matrix Product States

We give a new thought for constructing long-range quantum correlation in quantum many-body systems. Our proposed composite parity-conserved matrix product state has long-range quantum correlation only for two spin blocks where their spin-block length larger than 1 compared to any subsystem only having short-range quantum correlation, and we investigate quantum correlation properties of two spin blocks varying with environment parameter and spacing spin number. We also find that the geometry quantum discords of two nearest-neighbor spin blocks and two next-nearest-neighbor spin blocks become smaller and for other conditions the geometry quantum discord becomes larger than that in any subcomponent, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation compared to the corresponding classical correlation and total correlation having no any characteristic of regulation. For nearest-neighbor and next-nearest-neighbor all the correlations take their maximal values at the same points, while for other conditions no whether for spacing same spin number or for different spacing spin numbers all the correlations taking their maximal values are respectively at different points which are very close. We believe that our work is helpful to comprehensively and deeply understand the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems; and further helpful for the classification, the depiction and the measure of quantum correlation of quantum many-body systems.     

Peculiar Quantum Phase Transitions and Hidden Supersymmetry in a Lipkin-Meshkov-Glick Model

In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin- Meshkow-Glick model： an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a flrst-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another flrst-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.     

Quantum Probing Topological Phase Transitions by Non‐Markovianity

Understanding the physical significance and probing the global invariants characterizing quantum topological phases in extended systems is a main challenge in modern physics with major impact in different areas of science. Here, a quantum‐information‐inspired probing method is proposed where topological phase transitions are revealed by a non‐Markovianity quantifier. The idea is illustrated by considering the decoherence dynamics of an external read‐out qubit that probes a Su–Schrieffer–Heeger (SSH) chain with either pure dephasing or dissipative coupling. Qubit decoherence features and non‐Markovianity measure clearly signal the topological phase transition of the SSH chain.