Quantum Matter

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].

Tensor networks have been very successful for approximating quantum states that would otherwise require exponentially many parameters.

I will discuss how a similar compression can be achieved in models used to machine learn data, such as sets of images, by representing the fitting parameters as a tensor network. The resulting model achieves state-of-the-art performance on standard classification tasks. I will discuss implications for machine learning research, exploring which insights from physics could be imported into this field.

I will discuss the stability and breakdown of the topological classification of gapped ground states of non-interacting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions.  In our approach [1], the effects of interactions on the boundary gapless modes are encoded in terms of boundary dynamical masses. Breakdown of the non-interacting topological classification occurs when the quantum nonlinear sigma models for the boundary dynamical masses favor quantum disordered phases.  The non-interacting topological classification $Z$ in odd spatial dimensions is unstable and reduces to $Z_N$ that can be identified explicitly for any dimension and any defining symmetries.
[1] T. Morimoto, A. Furusaki, and C. Mudry, Phys. Rev. B 91, 235111 (2015).

I will review recent progress on theory of many-body localization, mostly focusing on properties of the many-body localized phase itself.

I will discuss explicit construction of effective Hamiltonians governing the dynamics of conserved quantities.  The analysis reveals several inequivalent length scales in the system, some of which do not appear to diverge on the approach to the thermalized phase.

Experimental protocols to measure these length scales will also be discussed.

Numerical results suggest that the quantum Hall effect at {\nu} = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at {\nu} =

5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.

We numerically investigate the expansion of clouds of hard-core bosons in a 2D square lattice using a matrix-product state based method. This non-equilibrium setup is induced by quenching a trapping potential to zero and is specifically motivated by an experiment with ultracold atoms [1]. As the anisotropy for hopping amplitudes in different spatial directions is varied from 1D to 2D, we observe a crossover from a fast ballistic expansion in the 1D limit to much slower dynamics in the isotropic 2D lattice [2].

Introducing a site-dependent disorder potential allows to study many body localization (MBL). In a very recent experiment, the melting of a domain wall gave evidence for an MBL transition in 2D [3]. We study 1D and quasi-1D models, for which the phase diagram in the presence of disorder is known, such as the Anderson insulator, Aubry-Andre model and interacting fermions in 1D and on a two-leg ladder [4]. By considering several observables, we demonstrate that the domain wall melting can indeed yield quantitative information on the transition from an ergodic to the MBL phase as a function of disorder.

[1] J. P. Ronzheimer et al., PRL 110, 205301 (2013) [2] J. Hauschild et al., PRA 92, 053629 (2015) [3] J. Choi et al., arXiv:1604.04178 (2016) [4] J. Hauschild et al., in preparation

Topological insulators (TIs) are a recently discovered state of matter characterized by an “inverted” band structure driven by strong spin-orbit coupling. One of their most touted properties is the existence of robust "topologically protected" surface states.  I will discuss what topological protection means for transport experiments and how it can be probed using the technique of time-domain THz spectroscopy applied to thin films of Bi2Se3.  By measuring the low frequency optical response, we can follow their transport lifetimes as we drive these materials via chemical substitution through a quantum phase transition into a topologically trivial regime[1].  I will then discuss our work following the evolution of the response as a function of magnetic field from the semi-classical transport regime[2] to the quantum regime[3].  In the semi-classical regime, an anomalous increase of the transport scattering rate was observed at high field, which contribute from electron-phonon interaction[2].  In the highest quality samples[3,4], we observe a continuous crossover from a low field regime where the response is given by semi-classical transport and observed in the form of cyclotron resonance to a higher field quantum regime[3].  In the later case, we find evidence for Faraday and Kerr rotation angles quantized in units of the fine structure constant[3].  This quantized rotation angle can be seen as evidence for a novel magneto-electric of the TI’s surface e.g. the much heralded axion electrodynamics of topological insulators.  Among other aspects this give a purely solid-state measure of fine structure constant[3].

1. Wu, et al, Nat. Phys. 9, 410 (2013).

2. Wu, et al, Phy. Rev. Lett. 115, 217602  (2015).

3. Wu, et al, arXiv. 1603.04317 (2016)

4. Nikesh, et al, Nano. Lett. 15, 8245 (2015)

Quantum-critical strongly correlated electron systems are predicted to feature universal collision-dominated transport resembling that of viscous fluids. Investigation of these phenomena has been hampered by the lack of known macroscopic signatures of electron viscosity. Here we identify vorticity as such a signature and link it with a readily verifiable striking macroscopic DC transport behavior. Produced by the viscous flow, vorticity can drive electric current against an applied field, resulting in a negative nonlocal voltage. The latter may play the same role for the viscous regime as zero electrical resistance does for superconductivity. Besides offering a diagnostic which distinguishes viscous transport from ohmic currents, the sign-changing electrical response affords a robust tool for directly measuring the viscosity-to-resistivity ratio. Strongly interacting electron-hole plasma in high-mobility graphene affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.

Levitov and Falkovich, Nature Physics, 22 Feb 2016