Session S12: Strongly Correlated Quantum Phases

Fate of the Fermionic Quasiparticles at the Electronic Nematic-Smectic Quantum Critical Point

We use the order-parameter theory of the electronic nematic- smectic transition of the fermionic liquid crystal phases, discussed in the previous talk, to study the effect of the low energy bosonic modes on the fermionic quasiparticles using RPA. Both the continuous model, which has a continuous rotational symmetry, and the lattice model, which has a discrete point group symmetry are studied. We find that at the nematic-smectic critical point, due to the critical smectic fluctuations, the dynamics of the fermionic quasiparticles near several points on the Fermi surface, which eventually become gapped under the development of CDW order, are not governed by a Landau Fermi liquid. Surprisingly, the fermions in the smectic phase also form a non-Fermi liquid. The transition between the quantum liquid crystal phases and the insulating CDW state is also discussed.   

Novel Transitions in S=1 Spinor Condensates and XY Ashkin-Teller Universality

We study spin-1 polar spinor condensates with magnetic anisotropy, in two spatial dimensions at finite temperatures. The topological binding of vorticity to nematic disclinations leads to a rich phase diagram, which is captured by a U(1) version of the Ashkin-Teller model. In particular, a ``cascaded'' Kosterlitz-Thouless critical point, with two diverging scales, is predicted. Numerical simulations are performed to check our picture.   

Theory of the Nematic-Smectic Quantum Phase Transition in Strongly Correlated Electronic Systems

The quantum liquid crystal phases were first proposed in Ref. [1], as one possible way to understand the high $T_c$ superconductors. We discuss the quantum phase transition between a quantum nematic metallic state (a uniform state which breaks spontaneously the point group symmetry) to an electron metallic smectic state (a state with a unidirectional charge density wave order), and construct an order-parameter theory. Its static part has the McMillan-DeGennes form of the classical smectic-nematic phase transition, while its quantum dynamics is dominated by the coupling to the electronic quasiparticles. Both, commensurate and incommensurate cases are studied. The spectrum of the nematic phase has low energy ``fluctuating stripes''. We also provide evidence that, contrary to the classical case, the gauge-type of coupling between the nematic and smectic at the critical point is irrelevant at this QCP. We discuss the relevance of these ideas to the phenomenology of the high $T_c$ superconductors. [1] S. A. Kivelson, E. Fradkin and V. J. Emery, nature 393, 550, 1998.   

Universal Scaling in the Fan of an Unconventional Quantum Critical Point

We present the results of stochastic series expansion Quantum Monte Carlo simulations on a 2D S=1/2 Heisenberg model with additional four-spin interaction -- the so-called `JQ' model [1]. Using extensive simulations on lattice sizes containing in excess of 10$^4$ spins, we examine the claim that the observed N\'eel to valence-bond-solid (VBS) quantum phase transition is consistent with the `deconfined' quantum criticality scenario. We discuss finite-temperature properties of the conjectured quantum critical fan [2], including scaling behavior, the calculation of universal critical exponents, and the apparent emergence of a global U(1) symmetry in the VBS order parameter. Finally, we consider several extensions of the model that may help give further insight into the nature of this unconventional quantum phase transition. \newline \newline [1] Sandvik, Phys. Rev. Lett. 98, 227202 (2007). \newline [2] Melko and Kaul, arXiv:0707.2961.   

Quantum critical scaling behavior of deconfined spinons

The quantum scaling behavior of deconfined spinons for a class of field theoretic models of quantum antiferromagnets is considered. The competition between the hedgehogs and the Berry phases is discussed from a renormalization group perspective. An important result following from our analysis is the computation of the anomalous dimension for the decay of spin correlations. Our results confirm the expectation that the transition from a N\'eel to a valence-bond solid state belongs to a completely new universality class.   

Monte-Carlo simulations of su(2) symmetric deconfined criticality action

We discuss results of Monte Carlo simulations of su(2) symmetric deconfined criticality action in $CP^1$ formulation proposed by T. Senthil,et. al, Science {\bf 303}, 1490 (2004). Using high-temperature expansion we reformulate the partition function in terms of J-currents. The resulting configuration space is explicitly su(2) symmetric. Critical behavior in the region of possible deconfined critical point (DCP) is addressed by the flow method [A.B.Kuklov, et.al., Annals of Physics {\bf 321},1602(2006)] mapping critical properties of a system with small values of the gauge interaction $g$ at large sizes to a system with large $g$ and small sizes. We observe data collapse on a single master curve with the flow toward fluctuation induced I order transition. The unlikely possibility of existence of the lower tricritical point separating I order transitions from the DCP line is assessed in terms of disruption of the flow collapse.   

Phase diagram of the anisotropic two-dimensional bilinear biquadratic spin-1 Heisenberg model

The anisotropic bilinear biquadratic Heisenberg model on a square lattice has been proposed to exhibit deconfined critical phenomena (DCP) based on QMC simulations and effective field theoretical studies [1, 2]. We investigate the phase transitions of the model using slave boson representation. Our mean field approach suggests a first order transition between the nematic and the disordered regime except at the tricritical SU(3) symmetric point. We will also discuss the relevance of our results to the DCP. \newline [1] T. Grover and T. Senthil, Phys. Rev. Lett. 98, 247202 (2007) \newline [2] K. Harada, N. Kawashima and M. Troyer, J. Phys. Soc. Jpn. 76, 013703 (2007)   

Generic mixed columnar-plaquette phases in Rokhsar-Kivelson models

We revisit the phase diagram of Rokhsar-Kivelson models, which are used in fields such as superconductivity, frustrated magnetism, cold bosons, and the physics of Josephson junction arrays. From an extended height effective theory, two simple generic phase diagrams are obtained. The first one is a first order transition scenario between the columnar and the plaquette phases, common in such models. The second, more exotic, exhibits a second order transition and contains a mixed phase that interpolates continuously between columnar and plaquette states. From exact diagonalization and Green's funtion Monte Carlo techniques, we present evidence that a realization of the latter scenario occurs in the Rokhsar-Kivelson square lattice Quantum Dimer model. This model, originally proposed in the context of high-temperature superconductivity, and its descendants have taken on a central role in the study of quantum systems incorporating a hard local constraint. By combining an analysis of the excitation gaps of different symmetry sectors with information on plaquette structure factors, we show the presence of a phase exhibiting both the plaquette and the columnar properties. This also presents a natural framework for resolving the disagreement between previous studies.   

An exact chiral spin liquid with non-Abelian anyons

We establish the existence of a ``chiral spin liquid'' (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle [1]. This state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSL's separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial CSL (Chern number $\pm 1$) obey non-Abelian statistics. \\ $[1]$ Hong Yao and Steven A. Kivelson, Phys. Rev. Lett. in Press.   

Non-abelian topological phases and unconventional criticality in a model of interacting anyons

Non-abelian topological phases have recently attracted considerable interest in the context of fault-tolerant quantum computation. However, such phases have only been established in a small set of microscopic models, one of which involves interacting spin-1/2 degrees of freedom on a honeycomb lattice (Levin, Wen 2005). In particular, this model supports quasiparticle excitations that can be described as so-called Fibonacci anyons. We have reformulated this model in terms of anyonic degrees of freedom and consider the case of interacting anyonic quasiparticles by adding a magnetic field term to the Hamiltonian. Our analysis of a quasi-one-dimensional ladder model not only shows the (extended) stability of the topological phase when perturbed by such local terms, but also demonstrates the role of topology in determining the exact nature of these phases. Interestingly, the magnetic field can drive a phase transition between two distinct topological phases. Numerically, we establish that this critical point can be described by a conformal field theory with central charge c=14/15. This observation has lead to an analytical understanding of this critical point which can be mapped to an exactly solvable transfer matrix representation in terms of a restricted-solid-on-solid (RSOS) model.   

Topological Mott Insulators

We consider extended Hubbard models with repulsive interactions on a Honeycomb lattice, and the transitions from the semi-metal to Mott insulating phases at half-filling. Due to the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spinful fermion models, respectively. The mean-field phase diagram is presented fluctuations are treated within the random phase approximation (RPA). Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.   

Critical liquid phases for frustrated bosons in two dimensions

An interesting question in strongly correlated systems is the possibility of a ``metallic'' bosonic liquid -- a quantum liquid phase of bosons that is neither superfluid nor Mott insulator. We present an attempt to construct such states using slave particle technique borrowed from theories of spin liquids; the approach can be also loosely viewed as a flux attachment treatment performed in the absence of time reversal breaking. We describe properties of thus constructed boson liquid states, which support gapless boson excitations residing on ``Bose surfaces'' in the momentum space and exhibit power law correlations in various properties. We also suggest a promising model Hamiltonian of hard-core bosons hopping on a square lattice and with frustrating ring exchanges which may have such a phase.   

Pseudogap in strongly interacting and strongly disordered systems

The interplay of disorder and correlation is known to give rise to anomalies in the density of states at the chemical potential of quantum and classical systems. In particular, in the quantum case, the diagrammatic calculation of Altshuler and Aronov predicts a pseudo-gap for the case of a weakly disordered and weakly interacting metal. Here we report a numerical study suggesting that such anomalies are present also in the case of strongly interacting and strongly disordered systems. We consider the Hubbard model in the presence of diagonal disorder and diagonalize small clusters (up to 12 sites) in the framework of a grand canonical scheme involving twisting the boundary condition. For a given interaction and disorder strength we observe the formation of a pseudo-gap whose shape and depth is largely insensitive to the particle density. For a given particle density the pseudo-gap gets deeper as the interaction and the disorder are increased.   

Bose Metal Phase from Inhomogeneous Flow

Numerous experiments report a Bose Metal phase between the Superconducting (S) and the Insulating (I) phases at an SI transition. [1,2] However, theoretically the origin of the corresponding dissipation remains unclear. We propose a picture in which inhomogeneous superconducting flow occurs in channels/filaments, defined by islands of localized Bose Glass. The superconducting bosons interact with the localized bosons of the Bose Glass via the Coulomb interaction. This Coulomb drag generates an effective dissipation for the superflow. We developed a new numerical technique to simulate superconductivity by inertial dynamics and a current generator. We found a Bose Metal phase in a finite range of the disorder, bracketed by the superconducting and insulating phases. The noise spectrum was also determined and compared to recent experiments. \newline \newline [1] H.M. Jaeger, D.B. Haviland, B.G. Orr and A.M. Goldman, Phys. Rev. B 40, 182 (1989). \newline [2] A. Yazdani and A. Kapitulnik, Phys. Rev. Lett. 74, 3037 (1995); M. Steiner, N. Breznay and A. Kapitulnik, arxiv: 0710.1822.   

Double Occupancy in low-energy theoreis of doped Mott insulators

We review how a proper low-energy theory can be constructed for the Hubbard model by explicitly integrating over the degrees of freedom far away from the chemical potential. A surprsing feature of the exact low-energy theory is the emergence of an elementary charge 2e boson which mediates double occupancy much below the Mott scale. We show that within the standard canonical transformation formalismused to derive the $t-J$ model from the Hubbard model, a similar feature (double occupancy below the Mott scale) appears ONLY if the electron creation and annihilation operators are properly transformed as well. By comparing precisely how the electron operators transform in both theories, we are able to show that the charge 2e boson mediates dynamical spectral weight transfer across the Mott gap. At half-filling, the interactions mediated by the charge 2e boson defeat the artificial local SU(2) symmetry found earlier in the projected $t-J$ model. \\ R. G. Leigh, P. Phillips and T. -P. Choy, Phys. Rev. Lett. {\bf 99} 46404 (2007); arxiv:07071554 (PRB, in press).