Quantum Matter

How does thermalization in quantum systems work? Naively, the unitary time evolution prevents thermalization, but one can easily show that in general quantum systems thermalize when brought into contact with a thermal bath. In noninteracting systems, the approach to the thermal value can be either ballistic or diffusive depending on particle statistics and bath temperature.

However, many systems cannot be thermalized when placed in a bath: glasses.

I will discuss a disorderfree model of an organic electronic glass that is formed through rapid supercooling. Geometric frustration and long-range interactions cause the Arrhenius-type freezing.

Quenched disorder can also lead to glassiness, a phenomenon known as many-body localization. In this case, thermalization is prevented by the existence of extensively many local integrals of motion. I will show how to compute these integrals of motion and their properties.

The frequency-dependent longitudinal and Hall conductivities — σ_xx and σ_xy — are dimensionless functions of ω/T in 2+1 dimensional CFTs at nonzero temperature. These functions characterize the spectrum of charged excitations of the theory and are basic experimental observables. We compute these conductivities for large N Chern-Simons theory with fermion matter. The computation is exact in the ’t Hooft coupling λ at N = ∞. We describe various physical features of the conductivity, including an explicit relation between the weight of the delta function at ω = 0 in σ_xx and the existence of infinitely many higher spin conserved currents in the theory. We also compute the conductivities perturbatively in Chern-Simons theory with scalar matter and show that the resulting functions of ω/T agree with the strong coupling fermionic result. This provides a new test of the conjectured 3d bosonization duality. In matching the Hall conductivities we resolve an outstanding puzzle by carefully treating an extra anomaly that arises in the regularization scheme used.  

When the wavefunction of a macroscopic system unitarily evolves from a low-entropy initial state, there is good circumstantial evidence it develops "branches", i.e., a decomposition into orthogonal components that can't be distinguished from the corresponding incoherent mixture by feasible observations, with each component a simultaneous eigenstate of preferred macroscopic observables.  Is this decomposition unique?  Can the number of branches decrease in time?

Answering these questions is hard because branches are defined only intuitively, much like early investigations of algorithms prior to the Church–Turing thesis.  A rigorous definition could give a speed up to certain non-stationary matrix-product state numerical simulations, as well as solve Kent's Set Selection problem in the consistent histories formalism, a 20-year-old open challenge in the foundations of quantum mechanics. I introduce some tentative definitions based on the idea of redundant information, and establishing a uniqueness theorems. A key counterexample is provided by the Shor error-correction code, which demonstrates that branch structure with robust, redundant records on macroscopic scales can hide incompatible (noncommuting) structure on microscopic scales.

We consider d=2 fermions at finite density coupled to a critical boson. In the quenched or Bloch-Nordsieck approximation, where one takes the limit of fermion flavors N_f→0, the fermion spectral function can be determined {exactly}. We show that one can obtain this non-perturbative answer thanks to a specific identity of fermionic two-point functions in the planar local patch approximation. The resulting spectrum is that of a non-Fermi liquid: quasiparticles are not part of the exact fermionic excitation spectrum of the theory. Instead one finds continuous spectral weight with power law scaling excitations. Moreover, at low energies there are three such excitations at three different Fermi surfaces, two with a low energy Green's function G∼(ω−v k)^−1/2 and one with G∼|ω+k|^−1/3. We proceed to study this model with a finite N_f but still neglecting fermionic loops with 3 or more vertices, motivated by multiloop cancellations at large k_F. We still find a non-Fermi liquid but with a different IR spectrum.

Experimentalists have recently been able to engineer non-trivial topological band structures using ultracold atoms in optical lattices.

Motivated by ongoing experimental efforts to tune interactions, we explore the interplay between strong correlations and topology in these systems. Focusing on the Haldane-Hubbard honeycomb model as an example, we show that its strongly interacting Mott limit exhibits various chiral magnetic orders, including a wide regime of triple-Q tetrahedral order. Incorporating an additional third-neighbour hopping frustrates and ultimately "quantum-melts" the tetrahedral magnetic order. From analysing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid with gapped semion excitations. Our numerical results suggest that this frustration induced melting may be realised as an exotic continuous quantum phase transition. Finally, we discuss recent results which point toward a common mechanism of realising chiral spin liquids through the continuous melting of non-coplanar magnetic "parent" states.

Incommensurate charge order is a phenomenon in which the electrons in a crystal attempt to order with a period irrationally-related to that of

the lattice spacing. In the first half of this talk I will present recent work [1] in which we demonstrate that incommensurately charge-ordered systems can lower their free energy by forming quasicrystals: slices through higher-dimensional crystals with properties lying between  periodicity and disorder. The result potentially greatly increases the number of known, naturally-occuring quasicrystals from the two present examples, both of which were found in the same Siberian meteorite. In the second half I will present work from an ongoing experimental collaboration in which atomically-resolved scanning tunneling microscopy and atomic force microscopy on semiconducting monolayers of molybdenum diselenide (MoSe2) see conducting edge states along one-dimensional mirror twin boundaries. Remarkably, these edge states then develop their own energy gap via charge ordering [2]. We see a number of features suggestive of incommensurate order. By employing a simple analytical model we demonstrate that the effect is in fact a result of fine-tuning between charge ordering and quantum well physics coming from the small system size (on the order of thirty atoms).

[1] F. Flicker and Jasper van Wezel, Physical Review Letters 115, 236401

(2015), Natural 1D Quasicrystals from Incommensurate Charge Order

[2] S. Barja et al., Nature Physics 12, 751-757 (2016), Charge density

wave order in 1D mirror twin boundaries of single-layer MoSe2

Dimer models have long been a fruitful playground for understanding topological physics. We introduce a new class -- termed Majorana-dimer models -- where the dimers represent pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian Ising quasiparticles, and a topological (p − ip) superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We present parent Hamiltonians for this phase and unambiguously identify the topological order from entanglement measurement of the ground-state manifold on torus.

Quantum many-body systems are challenging to study because of their exponentially large Hilbert spaces, but at the same time they are an area for exciting new physics due to the effects of interactions between particles. For theoretical purposes, it is convenient to know if such systems can be expressed in a simpler way in terms of some nearly-free quasiparticles, or more generally if one can construct a large set of operators that approximately commute with the system’s Hamiltonian. In this talk I will discuss two ways of using the entanglement spectrum to tackle these questions. In the first part, I will show that strongly disordered systems in the many-body localized phase have a universal power-law structure in their entanglement spectra. This is a consequence of their local integrability, and distinguishes such states from typical ground states of gapped systems. In the second part, I will introduce a notion of “interaction distance” and show that the entanglement spectrum can be used to quantify “how far” an interacting ground state is from a free

(Gaussian) state. I will discuss some examples of quantum spin chains and outline a few future directions.

[1] M. Serbyn, A. Michailidis, D. Abanin, Z. Papic, arXiv:1605.05737.

[2] C. J. Turner, K. Meichanetzidis, Z. Papic, and J. K. Pachos, arXiv:1607.02679.

One dimensional symmetry protected topological (SPT) phases are gapped phases of matter whose edges are degenerate if the Hamiltonian respects a particular symmetry. With their interacting classification having been understood since 2010, we would like to further our understanding by addressing the following two questions: (1) Is there a unified way of understanding some of the exactly soluble models for 1D SPTs? And (2) if we are given two arbitrary SPTs, can we predict the structure of the phase transition between them? The answers turn out to be surprisingly simple. The first is given by relating various models to the Kitaev chain, uncovering new facts about some well-known SPTs. As for the transition between two arbitrary SPTs, it is generically described by a free conformal field theory which is determined by the topological class of the gapped phases.

Magnetic skyrmions are highly mobile nanoscale topological spin textures. We show, both analytically and numerically, that a magnetic skyrmion of an even azimuthal winding number placed in proximity to an s-wave superconductor hosts a zero-energy Majorana bound state in its core, when the exchange coupling between the itinerant electrons and the skyrmion is strong. This Majorana bound state is stabilized by the presence of a spin-orbit interaction. We propose the use of a superconducting tri-junction to realize non-Abelian statistics of such Majorana bound states.

Strongly interacting quantum systems driven out of equilibrium represent a fascinating field where several questions of fundamental importance remains to be addressed [1].

These range from the dynamics of high-dimensional interacting models to the thermalization properties of quantum gases in continuous space.

In this Seminar I will review our recent contributions to some of the dynamical quantum problems which have been traditionally inaccessible to accurate many-body techniques.

I will first focus on the main methodological developments we devised in the past years.

In particular, I will describe the time-dependent Variational Monte Carlo method [2,3] and two notable classes of variational quantum states : the time-dependent Jastrow-Feenberg expansion, and the most recently introduced Neural-network Quantum States [4]. These states can achieve high (and controllable) accuracy both in one and higher dimensions.

Then, I will discuss specific applications to the problem of information spreading in both short- and long-ranged interacting quantum systems [3,5]. Finally, I will also discuss recent applications to thermalization properties of Lieb-Liniger quantum gases [6].