Quantum Matter

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

In my talk I will introduce the spin liquid phases that occur in kagome antiferromagnets, and discuss their physical origin that are closely related with the newly discovered symmetry protected topological phase (SPT). I will first present our numerical (DMRG) study on the kagome XXZ spin model that exhibits two distinct spin liquid phases, namely the chiral spin liquid and the kagome spin liquid (the groundstate of the nearest neighbor kagome Heisenberg model). Both phases extend from the extreme easy-axis limit, through

SU(2) symmetric point, to the pure easy-plane limit. The two phases are separated by a continuous phase transition. Motivated by these numerical results, I will then focus on the easy-axis kagome spin system, and reformulate it as a lattice gauge model. Such formulation enables us to achieve a controlled theoretical description for the spin liquid phases. We then show that the chiral spin liquid is indeed a gauged U(1) SPT phase. On the other hand, we also propose that the kagome spin liquid is a critical spin liquid phase, which can be considered as a gauged deconfined critical point between a SPT and a superfluid phase.

Recent theoretical and experimental efforts have been focused on the identification of excitations in quantum spin ice. Due to their relation to the magnetic monopoles of classical spin ice, their quantum counterparts, called spinons, are a highly sought-after manifestation of fractionalization in frustrated quantum magnets like Yb2Ti2O7. Of particular current interest is the quantum dynamics of spinons, namely, their modes of propagation and interaction with the strongly correlated spin background. To investigate this dynamics, we study excited quantum square ice, as captured by the spin-1/2 checkerboard-lattice XXZ model. We formulate effective free-spinon theories in the strong Ising coupling limit, with spinons either deconfined or artificially confined to nearest-neighbor distance, and calculate the corresponding approximate dynamic spin-structure factors (DSFs). We then evaluate the DSF of the fully interacting model exactly for clusters of up to 72 sites. The resulting spectra allow us to identify dispersive fingerprints of coherent spinon propagation in the correlated ``vacuum'' of quantum square ice within an extended low-energy regime. We thus provide unbiased evidence for the formation of coherent quasiparticles in quantum spin ice above the Ising gap.

When a classical system is driven through a continuous phase transition, its nonequilibrium response is universal and exhibits Kibble-Zurek scaling. We explore this dynamical scaling in the context of a three-dimensional topological magnet with fractionalized excitations, namely, the liquid-gas transition of the emergent mobile magnetic monopoles in dipolar spin ice. Using field-mixing and finite-size scaling techniques, we place the critical point of the liquid-gas line in the three-dimensional Ising universality class. We then demonstrate Kibble-Zurek scaling for sweeps of the magnetic field through the critical point. Unusually slow microscopic time scales in spin ice offer a unique opportunity to detect this universal nonequilibrium physics within current experimental capability.

Recent work suggests that a sharp definition of `phase of matter' can be given for some quantum systems out of equilibrium---first for many-body localized systems with time independent Hamiltonians and more recently for periodically driven or Floquet localized systems. We present a new family of driven localized Floquet phases, which are analogues of the 1d symmetry protected topological phases familiar from the equilibrium setting. We then propose a classification for such phases.
 

The structure of entanglement can yield new physical insights into strongly interacting quantum critical states. I’ll describe key properties of the entanglement entropy of conformal field theories (CFTs) in 2+1d. In particular, we’ll see that sharp corners in the entangling surface contribute a regulator-independent function that depends non-trivially on the corner angle. I’ll argue that in the smooth limit this function yields the 2-point function of the stress tensor. This sheds light on recent cutting edge simulations of the quantum critical Ising, XY and Heisenberg models. I’ll also present a new lower bound for this function. I will then generalize to Rényi entropies, which yields a simple procedure to extract the thermal entropy using corner entanglement of the groundstate alone. Connections will be made to CFTs in 1+1d and 3+1d, as well as to Lifshitz theories.

Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions enforces and protects emergent gapless excitations, and symmetry is intrinsically tied to the topological protection in a certain class. Namely, unless the symmetry is broken, the topological nature is intact. We show novel interplay phenomena between symmetry and topology in topological phase transitions associated with line-nodal superconductors. The interplay may induce an exotic universality class in sharp contrast to that of the phenomenological Landau-Ginzburg theory. Hyper-scaling violation and emergent relativistic scaling are main characteristics, and the interplay even induces unusually large quantum critical region. We propose characteristic experimental signatures around the phase transitions in three spatial dimensions, for example, a linear phase boundary in a temperature-tuning parameter phase-diagram. 

Based on first-principle calculations, we show that a family of nonmagnetic materials including TaAs, TaP, NbAs, and NbP are Weyl semimetals (WSM) without inversion centers. We find twelve pairs of Weyl points in the whole Brillouin zone (BZ) for each of them. In the absence of spin-orbit coupling (SOC), band inversions in mirror-invariant planes lead to gapless nodal rings in the energy-momentum dispersion. The strong SOC in these materials then opens full gaps in the mirror planes, generating nonzero mirror Chern numbers and Weyl points off the mirror planes. The transport properties obtained by the Boltzmann equation combined with the semiclassical treatments of the unique electronic structure in these materials will also be discussed in comparison with the most recent experimental data.

We studied a holographic superconductor model with a momentum relaxation by employing a linear massless scalar field, which is expected to play a role of impurity via holographic correspondence. By fixing a ratio of impurity/chemical potential, we observed the complex scalar field condensation depending on temperature and computed an electric, thermoelectric, and thermal conductivities. Interestingly, in the presence of the linear massless scalar field, Drude behaviour was shown near a zero frequency regime and the numerical data for the conductivities satisfied Ferrell-Glover-Tinkham (FGT) sum rule. We also numerically checked that the holographic Ward Identity is hold and tried to find if universal law such as Homes law or Uemura’s law is present in our model. However, Homes law was not discovered and Uemera’s law was seen when the charge of the scalar field is 3 and the ratio of the impurity/chemical potential is smaller than about 1/2. 

Long-range quantum entanglement is now being recognized as a key characteristic of many novel states of quantum matter. The description of this entanglement requires the introduction of emergent “gauge fields”, much like those found in Maxwell’s theory of light. I will highlight some recent experiments on the copper-based high temperature superconductors, and interpret them using theories of emergent gauge fields.

We introduce the spectrum bifurcation renormalization group (SBRG) as an improvement of the excited-state real space renormalization group (RSRG-X) for qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the full MBL phase. As a Hilbert-space preserving RG, the SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.