Quantum Matter

Unlike entanglement entropy and mutual information which may mix both classical and quantum correlations, entanglement negativity received extensive interest recently, for its merit of measuring the pure quantum entanglement in the system. In this talk, I will introduce the entanglement negativity in 2+1 dimensional topologically ordered phases. For a bipartitioned or tripartitioned spatial manifold, we show how the universal part of entanglement negativity depends on the presence of quasiparticles and the choice of ground states. Besides interpreting recent results in exactly solvable lattice models, we give new results on non-Abelian topologically ordered phases.

Condensed matter realizations of Majorana zero modes constitute potential building blocks of a topological quantum computer and thus have recently been the subject of intense theoretical and experimental investigation.  In the first part of this talk, I will introduce a new scheme for preparation, manipulation, and readout of these zero modes in semiconducting wires coated with mesoscopic superconducting islands.  This approach synthesizes recent materials growth breakthroughs with tools long successfully deployed in quantum-dot research, notably gate-tunable island couplings, charge-sensing readout, and charge pumping.  Guided by these capabilities, we map out numerous milestones that progressively bridge the gap between Majorana zero-mode detection and long-term quantum computing applications.  These include (1) detecting non-Abelian anyon ‘fusion rules’ in two complementary schemes, one based on charge sensing, the other using a novel Majorana-mediated charge pump, (2) validation of a prototype topological qubit, (3) braiding to demonstrate non-Abelian statistics, and (4) observing the elusive topological phase transition accompanying the onset of Majorana modes.  With the exception of braiding, these proposed experiments require only a single wire with as few as two islands, a setup already available in the laboratory.  In the second part of the talk, I will introduce a new class of 2D microscopic models---termed ‘Majorana-dimer models’---which generalize well-known quantum dimer models by dressing the bosonic dimers with pairs of Majorana modes.  These models host a novel interacting topological phase of matter which has the same bulk anyonic content as the chiral Ising theory, albeit with a fully gapped edge.  These seemingly contradictory statements can be reconciled by noting that our phase is inherently fermionic:  it can be understood as the product of an Ising phase with a topological p-ip superconductor.  Potential physical realizations of this exotic state via a lattice of strongly interacting Majorana modes will be discussed.

In this talk, I would introduce spontaneous nematicity in the background of fractional quantum Hall fluids where symmetry breaking phenomenon intertwined with topological phase of matter. The resulting nematic FQH state is characterized by an order parameter that represents these quadrupolar fluctuations, which play the role of fluctuations of the local geometry of the quantum fluid. We demonstrate that the low-energy effective theory of the nematic order parameter has z=2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the nondissipative Hall viscosity. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of the Girvin-MacDonald-Platzman mode collapses at the isotropic-nematic quantum phase transition. An interesting feature of the nematic phase is that it has topological defects carrying nontrivial braiding statistics and fractional charge inherited from the topological fluid nature. In addition, I would also mention the decorated nodal line condensation in pair density wave SC, where the topological phase emerges concurrently with symmetry recovery by decorated defect condensation.

Quantum phase transitions arise at zero temperature when ground state energy meets non-analyticity upon tuning a non-thermal parameter.

Physical properties around quantum critical points (QCPs) are of extensive current interests because the fierce competition between critical quantum and thermal fluctuations near the QCPs can strongly affect dynamics and thermodynamics, leading to unconventional physics.

Despite of its great interests, however, it remains challenge to analytically understand such real frequency dynamics in strongly-correlated quantum systems, even for the dynamics in the quantum systems of one spatial dimension.

In the talk, motivated by recent experimental progresses, we shall take the challenge via analytically exploring finite temperature dynamics at the QCP of 3(space)+1(time) quantum φ^4 model, and zero-temperature spin dynamics in the quantum critical regime of XXZ Heisenberg model.

During the exciting excursion, sophisticated but powerful theoretical tools were introduced, and a bunch of new physics beyond conventional pictures were discovered. At the end we shall also discuss the implication of our results for experiments in relevant materials and suggest proper future experimental setups to test our theoretical findings.

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.