Quantum Matter

We report on our recent progress to investigate materials classes exhibiting d+id superconductivity, where topologically nontrivial pairing phases can emerge. Specifically, motivated by recent experimental progress, we show that graphene doped to the van Hove regime can give rise to a plethora of interesting ordering instabilities such as spin density wave and superconductivity. As a function of system parameters such as doping and range of Coulomb interaction, we explain which instability is favored by the system, and analyze the effect of long-range interactions on superconductivity giving rise to a competition between singlet d+id and triplet f wave. We also outline our work in progress for other materials classes which we believe are promising to stabilize such interesting topological superconducting states of matter.

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) will emerge when electrons move in Landau levels. In this talk, I will show FQHE can emergy even in the absence of Landau levels in interacting fermion models and boson models. The non-interacting part of our Hamiltonian contains topologically nontrivial flat band.

Recently, we developed a user friendly scheme based on the quantum kinetic equation for studying thermal transport phenomena in the presence of interactions and disorder . This scheme is suitable for both a systematic perturbative calculation as well as a general analysis. We believe that this method presents an adequate alternative to the Kubo formula, which for thermal transport is rather cumbersome. We have applied this approach in the study of the Nernst signal in superconducting films above the critical temperature. We showed that the strong Nernst signal observed in amorphous superconducting films, far above Tc, is caused by the fluctuations of the superconducting order parameter. We demonstrated a striking agreement between our theoretical calculations and the experimental data at various temperatures and magnetic fields. My talk will include a general description of the quantum kinetic approach, but mainly I will concentrate on the Nernst effect in superconducting films. I will use this example to discuss some subtle issues in the theoretical study of thermal phenomena that we encountered while calculating the Nernst coefficient. In particular, I will explain how the Nernst theorem (the third law of thermodynamics) imposes a strict constraint on the magnitude of the Nernst effect.

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.

We will discuss the effect of non-equilibrium drive near a quantum critical point in itinerant electron systems. Non-equilibrium field theory is formulated in terms of the Keldysh functional integral. The renormalization group approach is used to study the universality class of the non-equilibrium phase transition in the steady state system. The role of the non-equilibrium drive in the quantum-classical crossover will be discussed using the example of the Hertz-Millis theory and the generalization thereof.

We consider one dimensional devices supporting a pair of Majorana bound states at their ends We firstly show [1] that edge Majorana bound modes allow for processes with an actual transfer of electronic material between well-separated points and provide an explicit computation of the tunnelling amplitude for this process. We then show [2] that these devices can produce remarkable Hanbury-Brown Twiss like interference effects between well separated Dirac fermions of pertinent energies: we find indeed that, at these energies, the simultaneous scattering of two incoming electrons or two incoming holes from the Majorana bound states leads exclusively to an electron-hole final state. This "anti-bunching" in electron-hole internal pseudospin space can be detected through a measure of current-current correlations. Finally, we show [2] that, by scattering appropriate spin polarized electrons from the Majorana bound states, one can engineer a non-local entangler of electronic spins useful for quantum information applications. [1] G. W. Semenoff and P. Sodano: J. Phys. B: At. Mol. Opt. Phys. 40, 1479 (2007); [2] S. Bose and P. Sodano: “Non-local Handbury- Brown Twiss Interferometry & Entanglement Generation from Majorana

The simulation of systems of anyons offers a significant challenge to the condensed matter physicist. These systems are presently of substantial theoretical and experimental interest due to their potential for universal quantum computation, but due to their non-trivial exchange statistics, the tools available for their study have been limited. In this talk, I will present a formalism whereby any existing tensor network algorithm may be adapted for use with both Abelian and non-Abelian anyons, culminating in our recent simulations of infinite 1-D chains of interacting anyons using the Multi-scale Entanglement Renormalisation Ansatz, or MERA, demonstrating that tensor network algorithms may be effectively employed in the study of anyonic systems.