Quantum Matter

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.

In the rst part of this talk I will give a brief introduction to the variational class of continuous
matrix product states (cMPS). Then I will present a time evolution algorithm for cMPS with periodic
boundary conditions. In the second part, I will explain how to apply this method to simulate
atomtronic circuits. In particular, I will show results for persistent currents in an interacting bose
gas rotating in a ring shaped trap in the presence of an arti cial U(1) gauge potential.

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.

In this talk, I present a new framework for topologically ordered gapped ground states in 2+1 spacetime dimensions (which generalizes to higher dimensions) using tensor networks. We will see that topological order can exist in tensor network states (TNS), if the local tensor satisfies certain axioms which we call MPO (matrix product operator)-injectivity and pulling through. We then continue with examples, and see how renormalization fixed point models in the literature (Levin-Wen models, etc.) can be covered in this framework. If time permits, we finish with a discussion of excitations and the generalization to higher dimensions.

We investigate the properties of Chern-Simons theory coupled to massive fermions at finite density. In the large N limit, this is solvable to all orders in the coupling and we use this as a playground for investigating the behavior of strongly correlated condensed matter systems. At low temperatures the system enters a Fermi liquid state whose features may be compared to the phenomenological theory of Landau Fermi liquids and our analysis indicates the need to augment this framework to properly characterize parity odd transport. Furthermore, an investigation of the equation of state reveals novel phenomena at strong coupling. As the interaction strength is tuned to infinity, the system exhibits an extended intermediate regime in which the thermodynamics is described by neither Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.

We present an effective Z2 gauge theory that captures various competing phases in spin-1/2 kagome lattice antiferromagnets: the topological Z2 spin liquid (SL) phase, and the 12-site and 36- site valence bond solid (VBS) phases. Our effective theory is a generalization of the recent Z2 gauge theory proposed for SL phases by Wan and Tchernyshyov. In particular, we investigate possible VBS phases that arise from vison condensations in the SL. In addition to the 12-site and 36-site VBS phases, there exists 6-site VBS that is closely related to the symmetry-breaking valence bond modulation patterns observed in the recent density matrix renormalization group simulations. We find that our results have remarkable consistency with a previous study using a different Z2 gauge theory. Motivated by the lattice geometry in the recently reported vanadium oxyfluoride kagome antiferromagnet, our gauge theory is extended to incorporate lowered symmetry by inequivalent up- and down-triangles. We investigate effects of this anisotropy on the 12-site, 36-site, and 6-site VBS phases. Particularly, interesting dimer melting effects are found in the 36-site VBS. We discuss the implications of our findings and also compare the results with a different type of Z2 gauge theory used in previous studies.