arXiv subjects

Ashvin Vishwanath

Publications and source records attributed to Ashvin Vishwanath.

282 records · Page 16Linked to original sources

arXiv2004

Deconfined criticality critically defined

We describe characteristic physical properties of the recently introduced class of deconfined quantum critical points. Using some simple models, we highlight observables which clearly distinguish such critical points from those described by the conventional Landau-Ginzburg-Wilson framework: such a distinction can be made quite precisely even though both classes of critical points are strongly coupled, and neither has sharp quasiparticle excitations. We also contrast our classification from proposals by Bernevig et al. (cond-mat/0004291) and Yoshioka et al. (cond-mat/0404427).

cond-mat.str-el↗

arXiv2004

Extending Luttinger's theorem to Z(2) fractionalized phases of matter

Luttinger's theorem for Fermi liquids equates the volume enclosed by the Fermi surface in momentum space to the electron filling, independent of the strength and nature of interactions. Motivated by recent momentum balance arguments that establish this result in a non-perturbative fashion [M. Oshikawa, Phys. Rev. Lett. {\bf 84}, 3370 (2000)], we present extensions of this momentum balance argument to exotic systems which exhibit quantum number fractionalization focussing on $Z_2$ fractionalized insulators, superfluids and Fermi liquids. These lead to nontrivial relations between the particle filling and some intrinsic property of these quantum phases, and hence may be regarded as natural extensions of Luttinger's theorem. We find that there is an important distinction between fractionalized states arising naturally from half filling versus those arising from integer filling. We also note how these results can be useful for identifying fractionalized states in numerical experiments.

cond-mat.str-el↗

arXiv2004

Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids

We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transitions between two such VBS phases is studied. In some cases, an interesting second order transition controlled by a fixed line with varying critical exponents if found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gapped spin-1/2 spinon excitations emerge right at the transition. The low energy physics of this critical point (upto marginally irrelevant interactions) contains just a free quadratically dispersing `photon'. The phase structure on one side of this continuous transition is very intricate consisting of a series of infinitely closely spaced further transitions in a `devil's staircase' form. Analogies with previous examples of deconfined quantum criticality are emphasized. Closely related transitions in single layer systems are explored. These are second order only at some multicritical points. The solvable Rokshar-Kivelson point of quantum dimer models of single layer systems is found to correspond to a very special non-generic multicritical point

cond-mat.str-el↗

arXiv2004

Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression

We study the effect of hedgehog suppression in the O(3) sigma model in D=2+1. We show via Monte Carlo simulations that the sigma model can be disordered while effectively forbidding these point topological defects. The resulting paramagnetic state has gauge charged matter with half-integer spin (spinons) and also an emergent gauge field (photons), whose existence is explicitly demonstrated. Hence, this is an explicit realization of fractionalization in a model with global SU(2) symmetry. The zero temperature ordering transition from this phase is found to be continuous but distinct from the regular Heisenberg ordering transition. We propose that these phases and this phase transition are captured by the {\it noncompact} $CP^1$ model, which contains a pair of bosonic fields coupled to a noncompact U(1) gauge field. Direct simulation of the transition in this model yields critical exponents that support this claim. The easy-plane limit of this model also displays a continuous zero temperature ordering transition, which has the remarkable property of being self-dual. The presence of emergent gauge charge and hence Coulomb interactions is evidenced by the presence of a finite temperature Kosterlitz-Thouless transition associated with the thermal ionization of the gauge charged spinons. Generalization to higher dimensions and the effects of nonzero hedgehog fugacity are discussed.

cond-mat.str-el↗

arXiv2003

Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm

We present the critical theory of a number of zero temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S = 1/2 square lattice antiferromagnet between the Neel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a second order quantum phase transition. The critical theory is not expressed in terms of the order parameters characterizing either state (as would be the case in Landau-Ginzburg-Wilson theory) but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half-filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z_2 spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.

cond-mat.str-el↗

arXiv2003

"Deconfined" quantum critical points

The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or more phases and usually breaks a symmetry of the Hamiltonian. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. In this paper we show that near second order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm. We present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional `confining' order parameters. Nevertheless, the critical theory contains a new emergent gauge field, and `deconfined' degrees of freedom associated with fractionalization of the order parameters. We suggest that this new paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems.

cond-mat.str-el↗

arXiv2003

Weak-Field Thermal Hall Conductivity in the Mixed State of d-Wave Superconductors

Thermal transport in the mixed state of a d-wave superconductor is considered within the weak-field regime. We express the thermal conductivity, $κ_{xx}$, and the thermal Hall conductivity, $κ_{xy}$, in terms of the cross section for quasiparticle scattering from a single vortex. Solving for the cross section (neglecting the Berry phase contribution and the anisotropy of the gap nodes), we obtain $κ_{xx}(H,T)$ and $κ_{xy}(H,T)$ in surprisingly good agreement with the qualitative features of the experimental results for YBa$_{2}$Cu$_{3}$O$_{6.99}$. In particular, we show that the simple, yet previously unexpected, weak-field behavior, $κ_{xy}(H,T) \sim T\sqrt{H}$, is that of thermally-excited nodal quasiparticles, scattering primarily from impurities, with a small skew component provided by vortex scattering.

cond-mat.supr-con↗

arXiv2002

Screening and Dissipation at the Superconductor-Insulator Transition Induced by a Metallic Ground Plane

We study localization phenomena in two dimensional systems of charged particles in the presence of a metallic ground plane with a particular focus on the superconductor-insulator transition. The ground plane introduces a screening of the long-range Coulomb interaction, and provides a source of dissipation due to the gapless diffusive electrons. The interplay of these two effects leads to interesting physical phenomena which are analysed in detail in this paper. We argue that the generic superconductor-insulator transition of charged particles in the presence of the ground plane may be controlled by a {\it fixed line} with variable critical exponents. This is illustrated by an explicit calculation in an appropriate $ε$ expansion. In contrast, the universal properties of the superconductor-Mott insulator transition in the clean limit at commensurate densities are shown to be unmodified by either the metal or the long-range Coulomb interaction. A similar fixed line can arise in the presence of a metallic ground plane for quantum Hall plateau transitions. Implications for experiments on Josephson-junction arrays and quantum Hall systems are described.

cond-mat.str-el↗

arXiv2001

Dirac Nodes and Quantized Thermal Hall Effect in the Mixed State of d-wave Superconductors

We consider the vortex state of d-wave superconductors in the clean limit. Within the linearized approximation the quasiparticle bands obtained are found to posess Dirac cone dispersion (band touchings) at special points in the Brillouin zone. They are protected by a symmetry of the linearized Hamiltonian that we call T_Dirac. Moreover, for vortex lattices that posess inversion symmetry, it is shown that there is always a Dirac cone centered at zero energy within the linearized theory. On going beyond the linearized approximation and including the effect of the smaller curvature terms (that break T_Dirac), the Dirac cone dispersions are found to acquire small gaps (0.5 K/Tesla in YBCO) that scale linearly with the applied magnetic field. When the chemical potential for quasiparticles lies within the gap, quantization of the thermal-Hall conductivity is expected at low temperatures i.e. kappa_{xy}/T = n[(pi k_B)^2/(3h)] with the integer `n' taking on values n=+2, -2, 0. This quantization could be seen in low temperature thermal transport measurements of clean d-wave superconductors with good vortex lattices.

cond-mat.supr-con↗

arXiv2000

Quantum Walk on the Line

Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example of a typical walk, the ``Hadamard walk''. We show that after t time steps, the probability distribution on the line induced by the Hadamard walk is almost uniformly distributed over the interval [-t/sqrt(2),t/sqrt(2)]. This implies that the same walk defined on the circle mixes in_linear_ time. This is in direct contrast with the quadratic mixing time for the corresponding classical walk. We conclude by indicating how our techniques may be applied to more general graphs.

quant-ph↗

arXiv2000

Luttinger Liquid Physics in the Superconductor Vortex Core

We study several aspects of the structure of vortices in conventional s-wave Type $II$ superconductors. It is well-known that there are low energy quasiparticles bound to the core of a vortex. We show that under certain conditions, these quasiparticles form a degenerate Fermi gas with a finite density of states at the Fermi energy. In three dimensional superconductors, the result is a one dimensional Fermi gas of quasiparticles bound to the core of a vortex line. As is usual in one dimensional systems, interactions between the quasiparticles lead to Luttinger liquid behaviour. This may be probed through STM tunneling into the vortex core. We further suggest that a novel Peierls-type instability in the shape of the vortex line may develop due to interactions between the quasiparticle gas and fluctuations in the vortex line shape.

cond-mat.supr-con↗

arXiv2000

Two dimensional anisotropic non Fermi-liquid phase of coupled Luttinger liquids

We show using bosonization techniques, that strong forward scattering interactions between one dimensional spinless Luttinger liquids (LL) can stabilize a phase where charge-density wave, superconducting and transverse single particle hopping perturbations are irrelevant. This new phase retains its LL like properties in the directions of the chains, but with relations between exponents modified by the transverse interactions, whereas, it is a perfect insulator in the transverse direction. The mechanism that stabilizes this phase are strong transverse charge density wave fluctuations at incommensurate wavevector, which frustrates crystal formation by preventing lock-in of the in-chain density waves.

cond-mat.str-el↗