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Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside the framework of statistical mechanics as they involve the breakdown of ergodicity. Here, we consider what general constraints can be imposed on the nature of eigenstate transitions due to the presence of disorder. We derive Harris-type bounds on the finite-size scaling exponents of the mean entanglement entropy and level statistics at the many-body localization phase transition using several different arguments. Our results are at odds with recent small-size numerics, for which we estimate the crossover scales beyond which the Harris bound must hold., Comment: 6 pages

We investigate the spin-spin correlation functions of Ising magnets at complex values of the temperature, T. For one-dimensional chain and ladder systems, we show the existence of a kind of helimagnetic order in the vicinity of contours where the leading two eigenvalues of the transfer matrix become equal in magnitude. We analyse the development of long-range order as the two-dimensional limit is approached, and find that there is rich structure in much of the complex-T plane. In particular, and contrary to the work of Fisher on this problem, the development of long-range order is actually associated with a proliferation of partition function zeros in a certain finite region of that plane containing the real-temperature magnetically ordered phase. The thermodynamic consequences of this are also discussed., Comment: 5 pages, 3 figures

We discuss the superconductor to normal phase transition in an infinite-layered type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally excited pancake vortices. We assume the dominant interaction between vortices in the same and in different layers is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group flow, is that the phase transition in this model is a Kosterlitz--Thouless transition despite being a three--dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence of this is that the jump in the measured in-plane superfluid stiffness, which is a universal quantity in 2d Kosterlitz-Thouless theory, will receive a small non--universal correction (of order 1% in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$). This overall picture places some claims expressed in the literature on a more secure analytical footing and also resolves some conflicting views., Comment: 16 pages, 2 figures; minor typos corrected, references added

We examine the possibility that the large Nernst signal observed in the pseudogap regime of hole-doped cuprates originates from quasiparticle transport in a state with d-density wave (DDW) order, proposed by S. Chakravarty et al. [Phys. Rev. B 63, 094503 (2001)]. We find that the Nernst coefficient can be moderately enhanced in magnitude by DDW order, and is generally of negative sign. Thus, the quasiparticles of the DDW state cannot account for the large and positive Nernst signal observed in the pseudogap phase of the cuprates. However, the general considerations outlined in this paper may be of broader relevance, in particular to the recent measurements of Bel et al. in NbSe_2 and CeCoIn_5 [Phys. Rev. Lett. 91, 066602 (2003); ibid. 92, 217002 (2004)]., Comment: 9 pages, 3 figures; published version

Quantum dimer models on bipartite lattices exhibit Rokhsar-Kivelson (RK) points with exactly known critical ground states and deconfined spinons. We examine generic, weak, perturbations around these points. In d=2+1 we find a first order transition between a ``plaquette'' valence bond crystal and a region with a devil's staircase of commensurate and incommensurate valence bond crystals. In the part of the phase diagram where the staircase is incomplete, the incommensurate states exhibit a gapless photon and deconfined spinons on a set of finite measure, almost but not quite a deconfined phase in a compact U(1) gauge theory in d=2+1! In d=3+1 we find a continuous transition between the U(1) resonating valence bond (RVB) phase and a deconfined staggered valence bond crystal. In an appendix we comment on analogous phenomena in quantum vertex models, most notably the existence of a continuous transition on the triangular lattice in d=2+1., Comment: 9 pages; expanded version to appear in Phys. Rev. B; presentation improved

We discuss fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies for extracting information concerning such local order from experiments are derived with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems - the exactly solvable one dimensional electron gas with an impurity, and a weakly-interacting 2D electron gas. We extensively review experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies. We adduce evidence that stripe correlations are widespread in the cuprates. Finally, we compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi liquid state, and strong coupling, in which the magnetism is associated with well defined localized spins, and stripes are viewed as a form of micro-phase separation. We present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates., Comment: 43 pages, 11 figures, submitted to RMP; extensively revised and greatly improved text; one new figure, one new section, two new appendices and more references

The ``band-structure'' of a disordered stripe array is computed and compared, at a qualitative level, to angle resolved photoemission experiments on the cuprate high temperature superconductors. The low-energy states are found to be strongly localized transverse to the stripe direction, so the electron dynamics is strictly one-dimensional (along the stripe). Despite this, aspects of the two dimensional band-structure Fermi surface are still vividly apparent., Comment: 10 pages, 11 figures

We study the properties of a quasi-one dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple charicature of a locally striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi liquid normal state. Even in this limit, ``d-wave like'' order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasi-particle spectrum, or gapless ``nodal'' quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity., Comment: 4 pages, 1 figure, 1 table new version; vastly improved figure caption