Quantum Matter

A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. In this talk I describe recent work showing that there are 6 new electronic topological insulators that have no non-interacting counterpart. Combined with the previously known band-insulators, these produce a total of 8 topologically distinct phases. Two of the new topological insulators have a simple physical description as Mott insulators in which the electron spins form spin analogs of the familiar topological band-insulator. The remaining are obtained as combinations of these two `topological paramagnets' and the topological band insulator. These 8 phases form a complete list of all possible interacting topological insulators, and are classified by a $\mathbb{Z}_2^3$ group-structure. As a necessary part of the talk I will also review progress in the theory of bosonic Symmetry Protected Topological phases in 3d.

We present a set of models which realize interacting topological phases. The models are constructed in 2 dimensions for a system with U(1)xU(1) symmetry. We demonstrate that the models are topological by measuring their Hall conductivity, and demonstrating that they have gapless edge modes. We have also studied the models numerically.

In this talk, I will present recent work aimed at tackling two cornerstone problems in the field of strongly correlated electrons---(1) conducting non-Fermi liquid electronic fluids and (2) the continuous Mott metal-insulator transition---via controlled numerical and analytical studies of concrete electronic models in quasi-one-dimension.  The former is motivated strongly by the enigmatic "strange metal" central to the cuprates, while the latter is pertinent to, e.g., the spin-liquid candidate 2D triangular
lattice organic materials \kappa-(BEDT-TTF)_{2}Cu_{2}(CN)_{3} and EtMe_{3}Sb[Pd(dmit)_{2}]_{2}.  In the first part of the talk, I will focus on point (1) and discuss our realization on the two-leg ladder of a novel non-Fermi liquid quantum phase---the "d-wave metal"---which we construct by placing the charge sector of the electronic system into a "Bose metal" with strong d-wave correlations.  Importantly, this phase is non-perturbative in that it cannot be accessed starting from free electrons and slowly turning on interactions.  Remarkably, we are able to realize this strange metal as the ground state of reasonable microscopic Hamiltonian by augmenting the t-J model with a simple, local four-site ring-exchange interaction.  In the second half of the talk, I will discuss recent work on various half-filled electronic models on the two-leg triangular strip in which we have identified a continuous Mott transition between a metal and "spin Bose metal", where the latter is a novel
Mott-insulating spin-liquid phase obtained from the former by gapping out only the overall charge mode at strong coupling. Our Mott transition is shown to be in the XY universality class and thus
constitutes a clear and direct quasi-1D analog of the elegant higher-dimensional scenario recently proposed by Senthil [1].  Finally, I will touch on the potential relevance of these studies to the actual 2D materials which inspired them:  the cuprates and the organics.

[1]  T. Senthil, PRB 78, 045109 (2008).

When a large number of quantum mechanical particles are put together and allowed to interact, various condensed matter phases emerge with macroscopic quantum properties. While conventional quantum phases like superfluids or quantum magnets can be understood as a simple collection of
single particle quantum states, recent discoveries of fractional quantum Hall or spin liquids states contain intrinsic entanglement among all the particles. To understand such unconventional phases requires unconventional methods. In this talk, I will discuss how the quantum information insights about many-body entanglement gives us a unique perspective and a powerful tool to study these
unconventional phases. In particular, starting from simple entanglement building blocks, we are able to construct new gapped quantum phases, classify all possible gapped phases in certain cases and obtain a better understanding of the structure of the phase diagram. With these progress, we expect the many-body entanglement point of view to play an important role in our effort to map the full quantum phase diagram, leading to breakthroughs in our understanding of gapless phases and phase transitions and in the development of numerical tools to simulate such systems.

The decomposition of the magnetic moments in spin ice into freely moving magnetic monopoles has added a new dimension to the concept of fractionalization, showing that geometrical frustration, even in the absence of quantum fluctuations, can lead to the apparent reduction of fundamental objects into quasi particles of reduced dimension [1]. The resulting quasi-particles map onto a Coulomb gas in the grand canonical ensemble [2]. By varying the chemical potential one can drive the ground state from a vacuum to a monopole crystal with the Zinc blend structure [3].

The condensation of monopoles into the crystallized state leads to a new level of fractionalization:
the magnetic moments appear to collectively break into two distinct parts; the crystal of magnetic charge and a magnetic fluid showing correlations characteristic of an emergent Coulomb phase [4].

The ordered magnetic charge is synonymous with magnetic order, while the Coulomb phase space is equivalent to that of hard core dimers close packed onto a diamond lattice [5]. The relevance of these results to experimental systems will be discussed.

[1] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature 451, 42 (2008).
[2] L. D. C. Jaubert and P. C. W. Holdsworth, Nature Physics 5, 258 (2009).
[3] M. Brooks-Bartlett, A. Harman-Clarke, S. Banks, L. D. C. Jaubert and P. C. W. Holdsworth, In Preparation, (2013).
[4] C. L. Henley, Annual Review of Condensed Matter Physics 1, 179 (2010).
[5] D. A. Huse, W. Krauth, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 91, 167004 (2003).