Session N45: Exotic Phases in Strongly Correlated Systems

Fractionalization in a strongly correlated exciton system

We show that fractionalized phases arise out of a strongly coupled exciton bose condensate in a multi-band insulator. Based on a world line picture of exciton, we demonstrate that the deconfinement phases can occur in a gauge theory of the exciton model despite an infinite bare gauge coupling. A world sheet of electric flux line in the emergent gauge theory is identified as a web of exciton world lines. It is shown that a deconfined U(1) gauge theory with ``photon'' and either fractionalized boson or fermion can emerge out of a single model depending on the coupling constants. The statistics and spin of the fractionalized particles are shown to be determined uniquely by the dynamics of the model. The exciton model can be numerically simulated without sign problem and some of our results will be shown.   

Criticality in correlated quantum matter

At quantum critical points (QCPs) quantum fluctuations occur on all length scales, from microscopic to macroscopic, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. But how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? We answer these questions by examining exact solutions of models of systems with strong electronic correlations and find that QCPs can influence physical properties at surprisingly high temperatures. As a powerful illustration of quantum criticality, we predict that the zero temperature superfluid density, $\rho_{s}(0)$, and the transition temperature, $T_{c}$, of the copper-oxide superconductors are related by $T_{c}\propto\rho_{s}(0)^y$, where the exponent $y$ is different at the two edges of the superconducting dome, signifying the presence of the respective QCPs. This relationship can be tested in high quality crystals.   

Deconfined quantum-criticality in a 2D $S=1/2$ Heisenberg model

The two-dimensional $S=1/2$ Heisenberg model including a four-spin interaction is studied using a ground state projector quantum Monte Carlo (QMC) method in the valence bond basis. The model is sign-problematic in standard QMC methods formulated in the $S^z$ basis, but not in the valence bond basis. The ground state is studied on lattices with up to $40 \times 40$ spins. The four-spin interaction is shown to suppress the antiferromagnetic order, leading to a phase transition into a valence-bond-solid (VBS) state. The finite-size scaling of the singlet-triplet gap (which can be calculated with the valence bond projector using an improved estimator) scales as $1/L$ at the transition point, indicating a quantum phase transition with dynamic exponent $z=1$. This, and a large spin-spin correlation exponent, $\eta \approx 0.4$, suggests that the transition is a {\it deconfined quantum-critical point}. This would then be the first example of a model Hamiltonian for which this exotic N\'eel--VBS quantum-criticality has been observed.   

Bilayer antiferromagnet with four-spin interaction

We investigate a spin-1/2 Heisenberg antiferromagnet with four-spin interaction on bilayer square and honeycomb lattices. In addition to the standard Neel and quantum disordered phases, these models can be expected to have a valence-bond-solid (VBS) phase [1]. Our aim is to locate the VBS phase and to investigate, in particular, a transition from quantum disorder to VBS. This is potentially a deconfined quantum critical point [1]. We use a recently introduced ground state projection Monte Carlo method which allows us to study these models without negative-sign problems [2].\hfill\break [1] A. Vishwanath et al, Phys. Rev. B {\bf 69}, 224416 (2004). \hfill\break [2] A. W. Sandvik, Phys. Rev. Lett. {\bf 95}, 207203 (2005).   

Simulations of Quantum Spin Models on 2D Frustrated Lattices

Algorithmic advances in quantum Monte Carlo techniques have opened up the possibility of studying models in the general class of the S=1/2 XXZ model (equivalent to hard-core bosons) on frustrated lattices. With an antiferromagnetic diagonal interaction (Jz), these models can be solved exactly with QMC, albeit with some effort required to retain ergodicity in the near-degenerate manifold of states that exists for large Jz. The application of the quantum (ferromagnetic off-diagonal) interaction to this classically degenerate manifold produces a variety of intriguing physics, including an order-by-disorder supersolid phase, novel insulating states, and possible exotic quantum critical phenomena. We discuss numerical results for the triangular and kagome lattices with nearest and next-nearest neighbor exchange interactions, and focus on the relevance of the simulations to related areas of physics, such as experiments of cold trapped atomic gasses and the recent theory of deconfined quantum criticality.   

Quantum phase transition from a valence bond crystal to an antiferromagnet

We use the recently proposed two-step density-matrix renormalization group to study a ground state phase transition from a dimerized phase to a N\'eel phase in a frustrated spatially anisotropic Heisenberg and $t-J$ models. We compute critical exponents for the gap and correlation functions.   

Calculations of Domain Wall and Z$_{4}$ Vortex Energies in the Dimerized Phase of J1-J2 Heisenberg Model

We develop a series expansion method to calculate the Domain Wall Energy per unit length and the Z$_{4}$ vortex energies in the dimerized phase of the J1-J2 Heisenberg Model. The energy difference between the state with and without domain walls is calculated by series expansions around two different dimer configurations. The calculations are used to study the transition away from the dimerized phase. These calculations are compared with other studies of the phase boundaries in this system.   

The nature of quantum phase transition in quantum compass model

In this work, we show that the quantum compass model in two dimension can be mapped to a fermionic model with local density interaction and the quantum phase transition point at the symmetric point Jx=Jz marks a first order phase transition.   

Quantum Nematic Phase in the Emery Model

We investigate one strong coupling regime of the Emery model of a CuO plane in the strong coupling limit first discussed in ref. [1]. In this regime the on-site repulsion energies are much larger than the inter site Coulomb repulsions and the hopping terms. By integrating out the copper sites, we mapped this model into an interacting fermionic model on an effective two-dimensional crossed-chains lattice. We will discuss the simpler case of spinless fermions on this effective lattice in the regime in which the residual interactions are weak. Using a mean-field approach, we discuss the isotropic-nematic phase transition in this system. We show that the nematic phase may exist even for infinitesimally weak interactions. We investigate this phase transition for a range of dopings, temperatures and interactions. For certain choice of parameters, the effective electronic states behave like those of a 2D square lattice model, but for some other choices, its properties are reminiscent of a quasi-one-dimensional system. \newline \newline [1] Steven A. Kivelson, Eduardo Fradkin, and Ted Geballe, PRB 69, 144505 (2004)   

No sliding in time

We analyse the following apparent paradox: As has been recently proved by Hastings, under a general set of conditions, if a \emph{local} Hamiltonian has a spectral gap above its (unique) ground state, all connected equal-time correlation functions of local operators decay exponentially with distance. On the other hand, statistical mechanics provides us with examples of 3D models displaying so-called sliding phases which are characterised by the algebraic decay of correlations within 2D layers and exponential decay in the third direction. Interpreting this third direction as time would imply a gap in the corresponding (2+1)D quantum Hamiltonian which would seemingly contradict Hastings' theorem. The resolution of this paradox lies in the non-locality of such a quantum Hamiltonian.   

Quantum dimer model on a two dimensional pyramid lattice.

We study the Rokhsar-Kivelson (RK) quantum dimer model on a two dimensional corner-sharing pyramid lattice. Contrast to other lattices such as square and triangular lattice, on the RK line (V=t, V' arbitrary), the dimer-dimer correlation is exact zero as long as dimers are a few lattice constants away from each other. More interestingly, a deconfined dimer liquid phase (or RVB phase) is found to the left of the RK line in the phase diagram. There are two kinds of confined valence bond crystal (VBC) states to the very left of the RVB phase. And there is a VBC state to the right of the RK line. Surprisingly, the spinor excitations are deconfined~within the model even though the underlining state breaks the translational symmetry and rotational symmetry.   

A doped interacting quantum dimer model on the square lattice

We introduce a generalized quantum dimer model [1] for interacting dimers on the square lattice [2] which can be mapped to generic 2D classical partition functions. More specifically, we show that the amplitudes of the exact ground state wavefunction are given by the Gibbs weights of a 2D classical doped interacting dimer model. We use this mapping to determine the phase diagram in the interaction - hole density plane. Analytically, we exploit a direct microscopic mapping of the classical dimer model on the square lattice to a special 8-vertex model and generalized Coulomb gases. Numerically, we use a novel rejection-free geometrical cluster algorithm [3] for classical interacting dimers on the square lattice, in the canonical ensemble. We also use simulations to study the system in the grand canonical ensemble. We discuss the structure of the phase diagram and its critical behavior. 1. D.S. Rokhsar and S.A. Kivelson, PRL 61, 2376 (1988), 2. F. Alet et al. PRL 94, 235702 (2005), 3. J. Liu and E. Luijten, PRL 92, 035504 (2004).   

Possible New Physics at Quantum Critical Points: Skyrmions as Elementary Excitations of $2+1$ D Antiferromagnets

It has recently been proposed that there are degrees of freedom intrinsic to quantum critical points that can contribute to quantum critical physics. We point out that intrinsic critical degrees of freedom exist quite generally below the upper critical dimension. We show that in $2+1$ D antiferromagnets skyrmion excitations are stable at criticality and identify them as the critical excitations.   

Possible New Physics at Quantum Critical Points: Skyrmions as critical Spin 1/2 Excitations of 2+1 D Antiferromagnets

We show that despite the absence of a Hopf term and zero Berry phase terms, the N\`eel ordered phase of $2+1$ D quantum antiferromagnets have spin 1/2 excitations, i.e. {\it spinons}. The spinons are skyrmion excitations of a topological nature. Since skyrmion gap is proportional to the spin stiffness, quantum criticality corresponds to skyrmion gap collapse. We speculate that skyrmions are relevant at criticality and are, perhaps, related to recent suggestions of critical fractionalization.   

Quartet condensation of fermions

We investigate quartet condensation in fermion systems with four internal states. Physical examples include spin-3/2 fermionic atoms, transition metal oxides with orbital degeneracy, bi-layered systems with electrons and holes and quadra-layer spin-polarized electron hole systems. We consider a simple SU(4) symmetric model in which the fermions interact among themselves with point attractive interactions. The effective free energy functional of the Cooper Pairs (CP) is found to contain attractive interactions among certain types of CP's. This will allow the CP's to form bound states or quartets. Using a variational calculation based on the Bogoliubov inequality, we find that the system may undergo quartet condensation which will suppress the CP instability. By tuning the interaction away from the SU(4) limit, a phase transition from quartet to CP condensation can occur.