Condensed Matter

We investigate the entanglement spectra of topological insulators which have gapless edge states on their spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to discontinuities in the trace of the single-particle entanglement spectrum, which we call a `trace index'. We find that any free-fermion topological insulator that exhibits spectral flow has a non-vanishing trace index, which provides us with a new description of topological invariants. In addition, we identify the signatures of spectral flow in the single-particle and many-body entanglement spectrum; in the process we present new methods to extract topological invariants and establish a connection between entanglement and quantum Hall physics in translationally invariant and disordered systems.

Time-reversal invariant band insulators can be separated into two categories: `ordinary' insulators and `topological' insulators. Topological band insulators have low-energy edge modes that cannot be gapped without violating time-reversal symmetry, while ordinary insulators do not. A natural question is whether more exotic time-reversal invariant insulators (insulators not connected adiabatically to band insulators) can also exhibit time-reversal protected edge modes. In 2 dimensions, one example of this is the fractional spin Hall insulator (essentially a spin-up and spin-down copy of a fractional quantum Hall insulator, with opposite effective magnetic fields for each spin). I will discuss another family of strongly interacting insulators, which exist in both 2 and 3 dimensions, that can have time-reversal protected edge modes. This gives a new set of examples of `fractional' topological insulators.

Strongly correlated electron systems are play grounds for exotic quantum states such as high Tc superconductivity, quantum spin liquids, non-fermi liquids and so on. Recently high Tc superconductivity has been observed in an iron based compound K2Fe4Se5. I will present a model and outline an effective theory [1] that describes physics of this complex system - a non linear O(3) sigma model in 2 + 1 dimensions coupled to Dirac fermions. Topological solitons and induced quantum numbers are well known in Skyrme model for protons and neutrons. In our context, we get topological baby Skyrmions with an induced charge 2e. Baby Skyrmions conduct themselves `super'.

We discuss bulk and holographic features of black hole solutions of 4D anti de Sitter Einstein-Maxwell-Dilaton gravity. At finite temperature the field theory holographically dual to these solutions has a rich and interesting phenomenology reminiscent of electron motion in metals: phase transitions triggered by nonvanishing VEV of scalar operators, non-monotonic behavior of the electric conductivities etc. Conversely, in the zero temperature limit the transport properties for these models show an universal behavior.

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasi-critical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.

I will discuss the growth of entanglement under a quantum quench at point contacts of simple fractional quantum Hall fluids and its relation with the measurement of local observables. Recently Klich and Levitov recently proposed that, for a free fermion system, the noise generated from a local quantum quench provides a measure of the entanglement entropy. In this work, I will examine the validity of this proposal in the context of a strongly interacting system, the Laughlin FQH states. We find that local quenching in fractional quantum Hall junctions gives time dependent correlation functions that have universal behavior on sufficiently long time and length scales. The growth of entanglement entropy and the noise generated by the quench are generally unrelated quantities.

The spin 1/2 Heisenberg model on a triangular lattice with interchain exchange, J', weaker than the intrachain exchange J, is a particularly well-studied frustrated magnet because of its relevance to Cs2CuCl4, which is thought to be in close proximity to a spin liquid phase. Although an incomensurate spiral state is stable for J'~J, a variet of theoretical studies find evidence for spin liquid behavior well before the decoupled chain limit, J'=0, is reached. However, a renormalization group approach found the surprising result that a collinear antiferromagnetic phase was stable for small J'/J. This talk will briefly review earlier studies and present new results on the relative stability of spiral, collinear and spin liquid phases.

Very recently, it has been recognized that excitations out of the ground state of materials known as spin ice can be viewed as magnetic monopoles, the magnetic analog to electric charges. Like electrons and positrons, these particles possess a charge of +Q or -Q and therefore attract or repel each other. Magnetic monopoles, however, can be accelerated using a magnetic field instead of an electric field. In this talk, I will report on experiments deep into the frozen state of the spin ice material holmium titanate where monopoles are few and far between and the material responds very slowly to a changing magnetic field. Taking advantage of the extremely sensitive magnetic field detector known as a superconducting quantum interference device (SQUID), we measure the rate at which the monopoles are created, move about and are eventually annihilated. A surprisingly simple law emerges at low temperatures, known as an Arrhenius law, suggesting that the generation of these magnetic charges requires an energy that does not change in temperature and for a yet unknown reason, is precisely 3 times the energy required to make a single, bare monopole.

Geometrical frustration in magnetic systems provides a rich playground to study the emergence of novel ground states. In systems where not all magnetic couplings can be simultaneously satisfied, conventional long range magnetic order is often precluded, or pushed to much lower emperature scales than would be expected from the strength of the magnetic interactions. Dy2Ti2O7 has a pyrochlore lattice, where the magnetic Dy ions lie on the vertices of corner sharing tetrahedra. The Dy magnetic moments are constrained by crystal fields to lie along local <111> axes, pointing towards or away from the tetrahedral centres. With a ferromagnetic interaction between nearest neighbours, the ground state for each tetrahedron has two spins pointing in and two out. Due to the number of possible ways of satisfying this constraint, the overall ground state is highly degenerate; in fact this system can be mapped onto the problem of water ice where each oxygen atom has two strongly bound and two weakly bound protons, leading the magnetic problem to be referred to as spin ice. Recent theoretical work in understanding the magnetic excitation in spin ice, where the spin flip excitations can be described in terms of magnetic monopoles. Bramwell et al., reported muon spin rotation measurements of spin ice which they interpreted in terms of this monopole picture. In contrast to the work of Bramwell et al., our muon spin relaxation measurements do not exhibit highly temperature dependent Arrhenius processes expected for monopoles. Instead we report temperature independent spin fluctuations well into the spin ice state and that the previous interpretations are incorrect.