Olexei I. Motrunich

Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in kappa-(ET)2Cu2(CN)3

We study triangular lattice spin-1/2 system with antiferromagnetic Heisenberg and ring exchanges using variational approach focusing on possible realization of spin-liquid states. Trial spin liquid wave functions are obtained by Gutzwiller projection of fermionic mean-field states and their energetics is compared against magnetically ordered trial states. We find that in a range of the ring exchange coupling upon destroying the antiferromagnetic order, the best such spin liquid state is essentially a Gutzwiller-projected Fermi sea state. We propose this spin liquid with a spinon Fermi surface as a candidate for the nonmagnetic insulating phase observed in the organic compound kappa-(ET)2Cu2(CN)3, and describe some experimental consequences of this proposal.

Emergent photons and transitions in the O(3) sigma model with hedgehog suppression

We study the effect of hedgehog suppression in the O(3) sigma model in D = 2 + 1. We show via Monte Carlo simulations that the sigma model can be disordered while effectively forbidding these point topological defects. The resulting paramagnetic state has gauge charged matter with half-integer spin (spinons) and also an emergent gauge field (photons), whose existence is explicitly demonstrated. Hence, this is an explicit realization of fractionalization in a model with global SU(2) symmetry. The zero-temperature ordering transition from this phase is found to be continuous but distinct from the regular Heisenberg ordering transition. We propose that these phases and this phase transition are captured by the noncompact CP1 model, which contains a pair of bosonic fields coupled to a noncompact U(1) gauge field. Direct simulation of the transition in this model yields critical exponents that support this claim. The easy-plane limit of this model also displays a continuous zero temperature ordering transition, which has the remarkable property of being self-dual. The presence of emergent gauge charge and hence Coulomb interactions is evidenced by the presence of a finite temperature Kosterlitz-Thouless transition associated with the thermal ionization of the gauge charged spinons. Generalization to higher dimensions and the effects of nonzero hedgehog fugacity are discussed.

Exotic Order in Simple Models of Bosonic Systems

We show that simple Bose Hubbard models with unfrustrated hopping and short range two-body repulsive interactions can support stable fractionalized phases in two and higher dimensions, and in zero magnetic field. The simplicity of the constructed models advances the possibility of a controlled experimental realization and novel applications of such unconventional states.

Infinite-randomness quantum Ising critical fixed points

We examine the ground state of the random quantum Ising model in a transverse field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG) scheme. For spatial dimensionality d=2, we find that at strong randomness the RG flow for the quantum critical point is towards an infinite-randomness fixed point, as in one dimension. This is consistent with the results of a recent quantum Monte Carlo study by Pich et al. [Phys. Rev. Lett. 81, 5916 (1998)], including estimates of the critical exponents from our RG that agree well with those from the quantum Monte Carlo. The same qualitative behavior appears to occur for three dimensions; we have not yet been able to determine whether or not it persists to arbitrarily high d. Some consequences of the infinite-randomness fixed point for the quantum critical scaling behavior are discussed. Because frustration is irrelevant in the infinite-randomness limit, the same fixed point should govern both ferromagnetic and spin-glass quantum critical points. This RG maps the random quantum Ising model with strong disorder onto a novel type of percolation/aggregation process.

Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J_1−J_2 Square Heisenberg Model

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5<J(2)/J(1)<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J(2)/J(1)<0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.

Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions

We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2+1) dimensions (QED_{3}) with N=1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED_{3} scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N=2 QED_{3}.

Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples

We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconductors in which the quasiparticle spin is not conserved. We analyze one-dimensional models with this RG and with elementary transfer matrix methods. We find that such models with broken spin rotation invariance generically lie in one of two topologically distinct localized phases. Close enough to the critical point separating the two phases, the system has a power-law divergent low-energy density of states (with a nonuniversal continuously varying power law) in either phase, due to quantum Griffiths singularities. This critical point belongs to the same infinite-disorder universality class as the one-dimensional particle-hole symmetric Anderson localization problem, while the Griffiths phases in the vicinity of the transition are controlled by lines of strong (but not infinite) disorder fixed points terminating in the critical point.

The half-filled Landau level:The case for Dirac composite fermions

All is well with particle-hole symmetry In an external magnetic field, the energy of an electron in a two-dimensional system takes discrete values, called Landau levels. At high enough fields, all electrons in a solid can fit in the lowest Landau level. If exactly half of that level is filled with electrons, standard theory predicts that a special fermion liquid phase will form that makes a distinction between the filled and empty states (particles and holes). A recent conjecture, in contrast, predicted a liquid consisting of massless Dirac particles that respects the symmetry between particles and holes. Geraedts et al. used sophisticated numerical methods to provide strong evidence for this conjecture. Science, this issue p. 197 Density matrix renormalization group calculations show that particle-hole symmetry is preserved in a half-filled Landau level. In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that “composite fermions”—bound states of an electron with two magnetic flux quanta—can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2kF backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.

Spin Bose-metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip

Recent experiments on triangular lattice organic Mott insulators have found evidence for a two-dimensional (2D) spin liquid in close proximity to the metal-insulator transition. A Gutzwiller wave function study of the triangular lattice Heisenberg model with a four-spin ring exchange term appropriate in this regime has found that the projected spinon Fermi sea state has a low variational energy. This wave function, together with a slave particle-gauge theory analysis, suggests that this putative spin liquid possesses spin correlations that are singular along surfaces in momentum space, i.e., “Bose surfaces.” Signatures of this state, which we will refer to as a “spin Bose metal” (SBM), are expected to manifest in quasi-one-dimensional (quasi-1D) ladder systems: the discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here, we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg triangular strip (zigzag chain). Using density matrix renormalization group (DMRG) supplemented by variational wave functions and a bosonization analysis, we map out the full phase diagram. In the absence of ring exchange the model is equivalent to the J_1-J_2 Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess singular wave vectors at particular “Bose points” (remnants of the 2D Bose surface) and allow us to identify this phase as the hoped for quasi-1D descendant of the triangular lattice SBM state. We use bosonization to derive a low-energy effective theory for the zigzag spin Bose metal and find three gapless modes and one Luttinger parameter controlling all power law correlations. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 valence bond solid or a period-4 chirality order, which we discover in the DMRG. Another interesting instability is into a spin Bose-metal phase with partial ferromagnetism (spin polarization of one spinon band), which we also find numerically using the DMRG.

d-wave correlated critical Bose liquids in two dimensions

We develop a description of a quantum liquid phase of interacting bosons confined in two dimensions that possesses relative d-wave two-body correlations. We refer to this stable quantum phase as a d-wave Bose liquid (DBL). The DBL has no broken symmetries, supports gapless boson excitations that reside on “Bose surfaces” in momentum space, and exhibits power-law correlation functions characterized by a manifold of continuously variable exponents. While the DBL can be constructed for bosons moving in the two-dimensional continuum, the state only respects the point group symmetries of the square lattice. On the square lattice, the DBL respects all symmetries and does not require a particular lattice filling. However, lattice effects do allow for the possibility of a second distinct phase, a quasilocal variant we refer to as a d-wave local Bose liquid (DLBL). Remarkably, the DLBL has short-range boson correlations and hence no Bose surfaces, despite sharing gapless excitations and other critical signatures with the DBL. Moreover, both phases are metals with a resistance that vanishes as a power of the temperature. We establish these results by constructing a class of many-particle wave functions for the DBL, which are time reversal invariant analogs of Laughlins quantum Hall wave function for bosons in a half-filled Landau level. A gauge theory formulation leads to a simple mean field theory, and a suitable N-flavor generalization enables incorporation of gauge field fluctuations to deduce the properties of the DBL/DLBL in a controlled and systematic fashion. Various equal-time correlation functions thereby obtained are in qualitative accord with the properties inferred from the variational wave functions. We also identify a promising microscopic Hamiltonian that might manifest the DBL or DLBL, and perform a variational energetics study comparing other competing phases, including the superfluid. We suggest how the d-wave Bose liquid wave function can be suitably generalized to describe an itinerant non-Fermi-liquid phase of electrons on the square lattice with a no-double-occupancy constraint, a d-wave metal phase.