Vadim Oganesyan

How to detect fluctuating stripes in the high-temperature superconductors

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.

Phenomenology of fully many-body-localized systems

Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, NY 10016, USA(Dated: August 20, 2014)We consider fully many-body localized systems, i.e. isolated quantum systems where all themany-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems areintegrable, with localized conserved operators. These localized operators are interacting pseudospins,and the Hamiltonian is such that unitary time evolution produces dephasing but not ‘flips’ of thesepseudospins. As a result, an initial quantum state of a pseudospin can in principle be recoveredvia (pseudospin) echo procedures. We discuss how the exponentially decaying interactions betweenpseudospins lead to logarithmic-in-time spreading of entanglement starting from nonentangled initialstates. These systems exhibit multiple different length scales that can be defined from exponentialfunctions of distance; we suggest that some of these decay lengths diverge at the phase transitionout of the fully many-body localized phase while others remain finite.

Quantum Theory of a Nematic Fermi Fluid.

We develop a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions. Explicit expressions are obtained for the small amplitude collective excitations in the ordered state; remarkably, the nematic Goldstone mode (the director wave) is overdamped except along special directions dictated by symmetry. At the quantum critical point we find a dynamical exponent of

Superconductors are topologically ordered

z=3,

Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality

implying stability of the Gaussian fixed point. The leading perturbative effect of the overdamped Goldstone modes leads to a breakdown of Fermi-liquid theory in the nematic phase and to strongly angle-dependent electronic self energies around the Fermi surface. Other metallic liquid-crystal phases, e.g., a quantum hexatic, behave analogously.

Energy transport in disordered classical spin chains

Abstract We revisit a venerable question: what is the nature of the ordering in a superconductor? We find that the answer is properly that the superconducting state exhibits topological order in the sense of Wen, i.e., that while it lacks a local order parameter, it is sensitive to the global topology of the underlying manifold and exhibits an associated fractionalization of quantum numbers. We show that this perspective unifies a number of previous observations on superconductors and their low lying excitations and that this complex can be elegantly summarized in a purely topological action of the “ BF ” type and its elementary quantization. On manifolds with boundaries, the BF action correctly predicts non-chiral edge states, gapped in general, but crucial for fractionalization and establishing the ground state degeneracy. In all of this the role of the physical electromagnetic fields is central. We also observe that the BF action describes the topological order in several other physically distinct systems thus providing an example of topological universality.

Mean-field theory for symmetry-breaking Fermi surface deformations on a square lattice

Conventional phase transitions are usually characterized by a change in a fundamental thermodynamic observable, e.g., in density when liquid changes to vapor. A theoretical study of a one-dimensional disordered quantum spin chain reveals a new class of quantum phase transitions that leave no such signatures and pins down their origin.

Formation of an electronic nematic phase in interacting fermion systems

We present a numerical study of the diffusion of energy at high temperature in strongly disordered chains of interacting classical spins evolving deterministically. We find that quenched randomness strongly suppresses transport with the diffusion constant becoming reduced by several orders of magnitude upon the introduction of moderate disorder. We have also looked for but not found signs of a classical many-body localization transition at any nonzero strength of the spin-spin interactions.

Towards a statistical theory of transport by strongly-interacting lattice fermions

We analyze a mean-field model of electrons with pure forward scattering interactions on a square lattice which exhibits spontaneous Fermi surface symmetry breaking with a d-wave order parameter: the surface expands along the kx-axis and shrinks along the ky-axis (or vice versa). The symmetry-broken phase is stabilized below a dome-shaped transition line Tc(mu), with a maximal Tc near van Hove filling. The phase transition is usually first order at the edges of the transition line, and always second order around its center. The d-wave compressibility of the Fermi surface is however strongly enhanced even near the first order transition down to zero temperature. In the weak coupling limit the phase diagram is fully determined by a single non-universal energy scale, and hence dimensionless ratios of different characteristic quantities are universal. Adding a uniform repulsion to the forward scattering interaction, the two tricritical points at the ends of the second order transition line are shifted to lower temperatures. For a particularly favorable choice of hopping and interaction parameters one of the first order edges is replaced completely by a second order transition line, leading to a quantum critical point.

Nernst effect, quasiparticles, and d -density waves in cuprates

We study the formation of an electronic nematic phase characterized by a broken point-group symmetry in interacting fermion systems within the weak coupling theory. As a function of interaction strength and chemical potential, the phase transition between the isotropic Fermi liquid and nematic phase is first order at zero temperature and becomes second order at a finite temperature. The transition is present for all typical, including quasi-two-dimensional, electronic dispersions on the square lattice and takes place for arbitrarily small interaction when at van Hove filling, thus suppressing the Lifshitz transition. In connection with the formation of the nematic phase, we discuss the origin of the first-order transition and competition with other broken symmetry states.