A mean field approach for string condensed states

We describe a mean field technique for quantum string (or dimer) models. Unlike traditional mean field approaches, the method is general enough to include string condensed phases in addition to the usual symmetry breaking phases. Thus, it can be used to study phases and phases transitions beyond Landau's symmetry breaking paradigm. We demonstrate the technique with a simple example: the spin-1 XXZ model on the Kagome lattice. The mean field calculation predicts a number of phases and phase transitions, including a z=2 deconfined quantum critical point.Comment: 10 pages + appendix, 15 figure

Gapless Fermions and Quantum Order

Using 2D quantum spin-1/2 model as a concrete example, we studied the relation between gapless fermionic excitations (spinons) and quantum orders in some spin liquid states. Using winding number, we find the projective symmetry group that characterizes the quantum order directly determines the pattern of Fermi points in the Brillouin zone. Thus quantum orders provide an origin for gapless fermionic excitations.Comment: 23 pages. LaTeX. Homepage http://dao.mit.edu/~we

Spin-charge Separation in Nodal Antiferromagnetic Insulator

In this paper, by using two dimensional (2D) Hubbard models with pi-flux phase and that on a hexagonal lattice as examples, we explore spin-charge-separated solitons in nodal antiferromagnetic (AF) insulator - an AF order with massive Dirac fermionic excitations (see detail in the paper). We calculate fermion zero modes and induced quantum numbers on solitons (half skyrmions) in the continuum limit, which are similar to that in the quasi one-dimensional conductor polyacetylene (CH)x and that in topological band insulator. In particular, we find some novel phenomena : thanks to an induced staggered spin moment, a mobile half skyrmion becomes a fermionic particle; when a hole or an electron is added, the half skyrmion turns into a bosonic particle with charge degree of freedom only. Our results imply that nontrivial induced quantum number on solitons may be a universal feature of spin-charge separation in different systems

Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

We find a series of possible continuous quantum phase transitions between fractional quantum Hall (FQH) states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at \nu = 2/3 and single-component systems at \nu = 8/3.Comment: 4 pages + ref

Quantum correlations in a cluster-like system

We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations. All these facts show that the system is topologically ordered. We also find a string order parameter to characterize the quantum phase transition. Besides, we investigate two-site correlations including entanglement, quantum discord and mutual information. We study the different divergency behaviour of the correlations. The quantum correlation decays exponentially in both topological and magnetic phases, and diverges in reversed power law at the critical point. And we find that in TQPT systems, the global difference of topology induced by dimension can be reflected in local quantum correlations.Comment: 7 pages, 6 figure

Adiabatic Preparation of Topological Order

Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms local order parameters. This type of order plays a key role in the theory of the fractional quantum Hall effect, as well as in topological quantum information processing. Here we show that a system of n spins forming a lattice on a Riemann surface can undergo a second order quantum phase transition between a spin-polarized phase and a string-net condensed phase. This is an example of a phase transition between magnetic and topological order. We furthermore show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by O(\sqrt{n}). This provides a physically plausible method for constructing a topological quantum memory. We discuss applications to topological and adiabatic quantum computing.Comment: 4 pages, one figure. v4: includes new error estimates for the adiabatic evolutio

Fractional Quantum Hall Effect and Featureless Mott Insulators

We point out and explicitly demonstrate a close connection that exists between featureless Mott insulators and fractional quantum Hall liquids. Using magnetic Wannier states as the single-particle basis in the lowest Landau level (LLL), we demonstrate that the Hamiltonian of interacting bosons in the LLL maps onto a Hamiltonian of a featureless Mott insulator on triangular lattice, formed by the magnetic Wannier states. The Hamiltonian is remarkably simple and consists only of short-range repulsion and ring-exchange terms.Comment: 7 pages, 1 figure. Published version

Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States

We study the physics of electron tunneling between multiple quantum dots and the edge of a quantum Hall state. Our results generalize earlier work [G. A. Fiete, W. Bishara, C. Nayak, Phys. Rev. Lett. 101, 176801 (2008)] in which it was shown that a single quantum dot tunnel coupled to a non-Abelian quantum Hall state can realize a stable multi-channel Kondo fixed point at low-energy. In this work, we investigate the physics of multiple dots and find that a rich set of possible low-energy fixed points arises, including those with non-Fermi liquid properties. Previously unidentified fixed points may also be among the possibilities. We examine both the situation where the dots are spatially separated and where they are in close proximity. We discuss the relation to previous work on two-impurity Kondo models in Fermi liquids and highlight new research directions in multiple quantum impurity problems.Comment: 12 pages, 2 figure

Spontaneous spin ordering of Dirac spin liquid in a magnetic field

The Dirac spin liquid was proposed to be the ground state of the spin-1/2 Kagome antiferromagnets. In a magnetic field $B$, we show that the state with Fermi pocket is unstable to the Landau level (LL) state. The LL state breaks the spin rotation around the axis of the magnetic field. We find that the LL state has an in-plane 120$^{\circ}$ $q=0$ magnetization $M$ which scales with the external field $M\sim B^{\alpha}$, where $\alpha$ is an intrinsic calculable universal number of the Dirac spin liquid. We discuss the related experimental implications which can be used to detect the possible Dirac spin liquid phase in Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$.Comment: rewritten for clarit