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Register a new userTheory of smeared quantum phase transitions
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We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.
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Theories of photoinduced phase transitions have developed along with the progress in experimental studies, especially concerning their nonlinear characters and transition dynamics. At an early stage, paths from photoinduced local structural distortions to global ones are explained in classical statistical models. Their dynamics are governed by transition probabilities and inevitably stochastic, but they were sufficient to describe coarse-grained time evolutions. Recently, however, a variety of dynamics including ultrafast ones are observed in different electronic states. They are explained in relevant electronic models. In particular, a coherent lattice oscillation and coherent motion of a macroscopic domain boundary need appropriate interactions among electrons and lattice displacements. Furthermore, some transitions proceed almost in one direction, which can be explained by considering relevant electronic processes. We describe the history of theories of photoinduced phase transitions and discuss a future perspective.
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry connection around a closed loop). We compute these invariants (Chern numbers) and discuss their relation to QPT. In particular we show that Chern numbers can be used to label regions corresponding to different phases.
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What is the nature of these transitions and how can we characterize them? The usual Landau approach, with the concept of an order parameter that is finite in a symmetry broken phase is not useful in this context. Topological transitions do not imply a change of symmetry and there is no obvious order parameter. A crucial observation is that they are associated with a diverging length that allows a scaling approach and to introduce critical exponents which define their universality classes. At zero temperature the critical exponents obey a quantum hyperscaling relation. We study finite size effects at topological transitions and show they exhibit universal behavior due to scaling. We discuss the possibility that they become discontinuous as a consequence of these effects and point out the relevance of our study for real systems.
We find that the first-order quantum phase transitions~(QPTs) are characterized by intrinsic jumps of relevant operators while the continuous ones are not. Based on such an observation, we propose a bond reversal method where a quantity $mathcal{D}$, the difference of bond strength~(DBS), is introduced to judge whether a QPT is of first order or not. This method is firstly applied to an exactly solvable spin-$1/2$ textit{XXZ} Heisenberg chain and a quantum Ising chain with longitudinal field where distinct jumps of $mathcal{D}$ appear at the first-order transition points for both cases. We then use it to study the topological QPT of a cross-coupled~($J_{times}$) spin ladder where the Haldane--rung-singlet transition switches from being continuous to exhibiting a first-order character at $J_{times, I} simeq$ 0.30(2). Finally, we study a recently proposed one-dimensional analogy of deconfined quantum critical point connecting two ordered phases in a spin-$1/2$ chain. We rule out the possibility of weakly first-order QPT because the DBS is smooth when crossing the transition point. Moreover, we affirm that such transition belongs to the Gaussian universality class with the central charge $c$ = 1.
Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics more general than those of bosons or fermions. Such anyons emerge as quasiparticles in fractional quantum Hall states and certain frustrated quantum magnets. Quantum liquids of anyons exhibit degenerate ground states where the degeneracy depends on the topology of the underlying surface. Here we present a novel type of continuous quantum phase transition in such anyonic quantum liquids that is driven by quantum fluctuations of topology. The critical state connecting two anyonic liquids on surfaces with different topologies is reminiscent of the notion of a `quantum foam with fluctuations on all length scales. This exotic quantum phase transition arises in a microscopic model of interacting anyons for which we present an exact solution in a linear geometry. We introduce an intuitive physical picture of this model that unifies string nets and loop gases, and provide a simple description of topological quantum phases and their phase transitions.
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