arXiv subjects

Kirill Shtengel

Publications and source records attributed to Kirill Shtengel.

53 records · Page 3Linked to original sources

arXiv2008

Interferometry of non-Abelian Anyons

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at $ν=5/2$ and Read-Rezayi state at $ν= 12/5$.

quant-ph↗

arXiv2007

Decoherence of Anyonic Charge in Interferometry Measurements

We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges a and a' in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with a to give a'.

quant-ph↗

arXiv2006

Topological degeneracy of non-Abelian states for dummies

We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O. and T. Senthil, Phys. Rev. Lett. 96, 060601 (2006)] which relates fraction- alization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61, 10267 (2000)] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p+ip superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.

cond-mat.mes-hall↗

arXiv2006

Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of `magnetic' vortices, leading to confinement of the elementary `charge' excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and discuss our results in the context of quantum computation applications.

cond-mat.stat-mech↗

arXiv2006

Probing Non-Abelian Statistics with QuasiParticle Interferometry

We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to FQH interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed nu=12/5 plateau.

cond-mat.mes-hall↗

arXiv2006

Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

In this letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et. al. are also addressed.

cond-mat.mes-hall↗

arXiv2005

No sliding in time

In this letter, we analyse the following apparent paradox: As has been recently proved by Hastings (cond-mat/0305505), under a general set of conditions, if a local Hamiltonian has a spectral gap above its (unique) ground state (GS), 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 (O'Hern et al., cond-mat/9904415) 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.

cond-mat.str-el↗

arXiv2004

An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase

We propose an extended Hubbard model on a 2D Kagome lattice with an additional ring-exchange term. The particles can be either bosons or spinless fermions . At a special filling fraction of 1/6 the model is analyzed in the lowest non-vanishing order of perturbation theory. Such ``undoped'' model is closely related to the Quantum Dimer Model. We show how to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate ``d-isotopy space'', a necessary precondition for for a certain type of non-Abelian topological order. Near the ``special'' values, $d = 2 \cos π/(k+2)$, this space is expected to collapse to a stable topological phase with anyonic excitations closely related to SU(2) Chern-Simons theory at level k.

cond-mat.str-el↗

arXiv2004

A Line of Critical Points in 2+1 Dimensions: Quantum Critical Loop Gases and Non-Abelian Gauge Theory

We (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models are critical for $d\leq \sqrt{2}$, where $d$ parametrizes the models; (5) note that for the special values $d=2\cos(π/(k+2))$, they are related to doubled level-$k$ SU(2) Chern-Simons theory; (6) conjecture that they are in the universality class of a non-relativistic SU(2) gauge theory; and (7) show that its one-loop $β$-function vanishes for all values of the coupling constant, implying that it is also on a critical line.

cond-mat.str-el↗

arXiv2004

Vertex Models and Random Labyrinths: Phase Diagrams for Ice-type Vertex Models

We propose a simple geometric recipe for constructing phase diagrams for a general class of vertex models obeying the ice rule. The disordered phase maps onto the intersecting loop model which is interesting in its own right and is related to several other statistical mechanical models. This mapping is also useful in understanding some ordered phases of these vertex models as they correspond to the polymer loop models with cross-links in their vulcanised phase.

cond-mat.stat-mech↗

arXiv2003

A Class of $P,T$-Invariant Topological Phases of Interacting Electrons

We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding statistics. $P$ and $T$ invariance are maintained by a `doubling' of the low-energy degrees of freedom which occurs naturally without doubling the underlying microscopic degrees of freedom. The simplest examples have been the subject of considerable interest as proposed mechanisms for high-$T_c$ superconductivity. One is the `doubled' version (i.e. two opposite-chirality copies) of the U(1) chiral spin liquid. The second example corresponds to $Z_2$ gauge theory, which describes a scenario for spin-charge separation. Our main concern, with an eye towards applications to quantum computation, are richer models which support non-Abelian statistics. All of these models, richer or poorer, lie in a tightly-organized discrete family. The physical inference is that a material manifesting the $Z_2$ gauge theory or a doubled chiral spin liquid might be easily altered to one capable of universal quantum computation. These phases of matter have a field-theoretic description in terms of gauge theories which, in their infrared limits, are topological field theories. We motivate these gauge theories using a parton model or slave-fermion construction and show how they can be solved exactly. The structure of the resulting Hilbert spaces can be understood in purely combinatorial terms. The highly-constrained nature of this combinatorial construction, phrased in the language of the topology of curves on surfaces, lays the groundwork for a strategy for constructing microscopic lattice models which give rise to these phases.

cond-mat.str-el↗

arXiv2003

Non-Abelian topological phases in an extended Hubbard model

We describe four closely related Hubbard-like models (models A, B, C and D) of particles that can hop on a 2D Kagome lattice interacting via Coulomb repulsion. The particles can be either bosons (models A and B) or (spinless) fermions (models C and D). Models A and C also include a ring exchange term. In all four cases we solve equations in the model parameters to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate ``d-isotopy space'' $\bar{V}_d$, 0<d<2. Near the ``special'' values, $d = 2 \cos π/k+2$, $\bar{V}_d$ should collapse to a stable topological phase with anyonic excitations closely related to SU(2) Chern-Simons theory at level k. We mention simplified models $A^-$ and $C^-$ which may also lead to these topological phases.

cond-mat.str-el↗

arXiv2003

1/f Noise in Electron Glasses

We show that 1/f noise is produced in a 3D electron glass by charge fluctuations due to electrons hopping between isolated sites and a percolating network at low temperatures. The low frequency noise spectrum goes as ω^{-α} with αslightly larger than 1. This result together with the temperature dependence of αand the noise amplitude are in good agreement with the recent experiments. These results hold true both with a flat, noninteracting density of states and with a density of states that includes Coulomb interactions. In the latter case, the density of states has a Coulomb gap that fills in with increasing temperature. For a large Coulomb gap width, this density of states gives a dc conductivity with a hopping exponent of approximately 0.75 which has been observed in recent experiments. For a small Coulomb gap width, the hopping exponent approximately 0.5.

cond-mat.dis-nn↗

arXiv2001

Microscopic Models of 2D Magnets with Fractionalized Excitations

We demonstrate that spin-charge separation can occur in two dimensions and note its confluence with superconductivity, topology, gauge theory, and fault-tolerant quantum computation. We construct a microscopic Ising-like model and, at a special coupling constant value, find its exact ground state as well as neutral spin 1/2 (spinon), spinless charge e (holon), and $Z_2$ vortex (vison) states and energies. The fractionalized excitations reflect the topological order of the ground state which is evinced by its fourfold degeneracy on the torus -- a degeneracy which is unrelated to translational or rotational symmetry -- and is described by a $Z_2$ gauge theory. Our model is related to the quantum dimer model and is a member of a family of topologically-ordered models, one of which is integrable and realizes the toric quantum error correction code.

cond-mat.str-el↗

arXiv2001

On the Current Carried by `Neutral' Quasiparticles

The current should be proportional to the momentum in a Galilean-invariant system of particles of fixed charge-to-mass ratio, such as an electron liquid in jellium. However, strongly-interacting electron systems can have phases characterized by broken symmetry or fractionalization. Such phases can have neutral excitations which can presumably carry momentum but not current. In this paper, we show that there is no contradiction: `neutral' excitations {\em do} carry current in a Galilean-invariant system of particles of fixed charge-to-mass ratio. This is explicitly demonstrated in the context of spin waves, the Bogoliubov-de Gennes quasiparticles of a superconductor, the one-dimensional electron gas, and spin-charge separated systems in 2+1 dimensions. We discuss the implications for more realistic systems, which are not Galilean-invariant.

cond-mat.str-el↗

arXiv1999

Intersecting Loop Models on Z^D: Rigorous Results

We consider a general class of (intersecting) loop models in D dimensions, including those related to high-temperature expansions of well-known spin models. We find that the loop models exhibit some interesting features - often in the ``unphysical'' region of parameter space where all connection with the original spin Hamiltonian is apparently lost. For a particular n=2, D=2 model, we establish the existence of a phase transition, possibly associated with divergent loops. However, for n >> 1 and arbitrary D there is no phase transition marked by the appearance of large loops. Furthermore, at least for D=2 (and n large) we find a phase transition characterised by broken translational symmetry.

cond-mat.stat-mech↗

arXiv1998

Critical Behavior for 2d Uniform and Disordered Ferromagnets at Self-Dual Points

We consider certain two-dimensional systems with self--dual points including uniform and disordered $q$-state Potts models. For systems with continuous energy density (such as the disordered versions) it is established that the self--dual point exhibits critical behavior: Infinite susceptibility, vanishing magnetization and power law bounds for the decay of correlations.

cond-mat.stat-mech↗