arXiv subjects

Ian Affleck

Publications and source records attributed to Ian Affleck.

At least 73 records · Page 4Linked to original sources

arXiv2012

The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state. Resource states can arise from ground states of carefully designed two-body interacting Hamiltonians. This opens up an appealing possibility of creating them by cooling. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states are the ground states of particularly simple Hamiltonians with high symmetry, and their potential use in quantum computation gives rise to a new research direction. Expanding on our prior work [T.-C. Wei, I. Affleck, and R. Raussendorf, Phys. Rev. Lett. 106, 070501 (2011)], we give detailed analysis to explain why the spin-3/2 AKLT state on a two-dimensional honeycomb lattice is a universal resource for measurement-based quantum computation. Along the way, we also provide an alternative proof that the 1D spin-1 AKLT state can be used to simulate arbitrary one-qubit unitary gates. Moreover, we connect the quantum computational universality of 2D random graph states to their percolation property and show that these states whose graphs are in the supercritical (i.e. percolated) phase are also universal resources for measurement-based quantum computation.

quant-ph↗

arXiv2012

Towards a Rigorous Proof of Magnetism on the Edges of Graphene Nano-ribbons

A zigzag edge of a graphene nanoribbon supports localized zero modes, ignoring interactions. Based mainly on mean field arguments and numerical approaches, it has been suggested that interactions can produce a large magnetic moment on the edges. By considering the Hubbard model in the weak coupling limit, U<<t, for bearded as well as zigzag edges, we argue for such a magnetic state, based on Lieb's theorem. Projecting the Hubbard interactions onto the flat edge band, we then prove that resulting 1 dimensional model has a fully polarized ferromagnetic ground state. We also study excitons and the effects of second neighbor hopping as well as a potential energy term acting on the edge only, proposing a simple and possibly exact phase diagram with the magnetic moment varying smoothly to zero. Finally, we consider corrections of second order in U arising from integrating out the gapless bulk Dirac excitations.

cond-mat.mes-hall↗

arXiv2012

General method for calculating the universal conductance of strongly correlated junctions of multiple quantum wires

We develop a method to extract the universal conductance of junctions of multiple quantum wires, a property of systems connected to reservoirs, from static ground-state computations in closed finite systems. The method is based on a key relationship, derived within the framework of boundary conformal field theory, between the conductance tensor and certain ground state correlation functions. Our results provide a systematic way of studying quantum transport in the presence of strong electron-electron interactions using efficient numerical techniques such as the standard time-independent density-matrix renormalization-group method. We give a step-by-step recipe for applying the method and present several tests and benchmarks. As an application of the method, we calculate the conductance of the M fixed point of a Y junction of Luttinger liquids for several values of the Luttinger parameter $g$ and conjecture its functional dependence on $g$.

cond-mat.str-el↗

arXiv2011

Crossover in the two-impurity Kondo model induced by direct charge tunneling

Quantum critical behavior in the two-impurity Kondo model requires the distinct separation of two scales, T_K >> T*, where T_K is the Kondo temperature and T* is the scale at which the system renormalizes away from the quantum critical point to a stable Fermi liquid fixed point. We provide a derivation of T* based on the renormalization group to lowest order. This result is confirmed by a numerical renormalization group (NRG) analysis which supplements the analytic derivation with additional quantitative precision. The form of the low-energy Fermi liquid fixed point is derived and subsequently confirmed by the NRG. We discuss implications for series double quantum dot systems.

cond-mat.mes-hall↗

arXiv2011

Transverse spectral functions and Dzyaloshinskii-Moriya interactions in XXZ spin chains

Recently much progress has been made in applying field theory methods, first developed to study X-ray edge singularities, to interacting one dimensional systems in order to include band curvature effects and study edge singularities at arbitrary momentum. Finding experimental confirmations of this theory remains an open challenge. Here we point out that spin chains with uniform Dzyaloshinskii-Moriya (DM) interactions provide an opportunity to test these theories since these interactions may be exactly eliminated by a gauge transformation which shifts the momentum. However, this requires an extension of these X-ray edge methods to the transverse spectral function of the xxz spin chain in a magnetic field, which we provide.

cond-mat.str-el↗

arXiv2011

Helium-4 Luttinger liquids in nanopores

We study the low temperature properties of a helium-4 fluid confined in nanopores, using large-scale Quantum Monte Carlo simulations with realistic He-He and He-pore interactions. In the narrow-pore limit, the system can be described by the quantum hydrodynamic theory known as Luttinger liquid theory with a large Luttinger parameter, corresponding to the dominance of solid tendencies and strong susceptibility to pinning by a periodic or random potential from the pore walls. On the other hand, for wider pores, the central region appears to behave like a Luttinger liquid with a smaller Luttinger parameter, and may be protected from pinning by the wall potential, offering the possibility of experimental detection of a Luttinger liquid.

cond-mat.stat-mech↗

arXiv2011

Kondo Temperature in Multilevel Quantum Dots

We develop a general method to evaluate the Kondo temperature in a multilevel quantum dot that is weakly coupled to conducting leads. Our theory reveals that the Kondo temperature is strongly enhanced when the intradot energy-level spacing is comparable to or smaller than the charging energy. We propose an experiment to test our result, which consists of measuring the size-dependence of the Kondo temperature.

cond-mat.str-el↗

arXiv2011

Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been intensively explored and shown to provide restricted computation. Here, we show that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal resource for measurement-based quantum computation.

quant-ph↗

arXiv2011

A semi-classical approach to electron spin resonance in quantum spin systems

We develop a semi-classical approximation to electron spin resonance in quantum spin systems, based on the rotor or non-linear sigma model. The classical time evolution is studied using molec- ular dynamics while random initial conditions are sampled using classical Monte Carlo methods. Although the approximation may be especially powerful in two dimensions, we apply it here to one- dimensional systems of large spin at intermediate temperatures, in the presence of staggered and uniform magnetic fields. We first test the validity of the semi-classical approximation by comparing the magnetization to quantum Monte Carlo results on S = 2 chains. Then we calculate the ESR spectrum, finding broad coexisting paramagnetic and spin wave resonances.

cond-mat.str-el↗

arXiv2010

How to find conductance tensors of quantum multi-wire junctions through static calculations: application to an interacting Y-junction

Conductance is related to dynamical correlation functions which can be calculated with \textit{time-dependent} methods. Using boundary conformal field theory, we relate the conductance tensors of quantum junctions of multiple wires to static correlation functions in a finite system. We then propose a general method for determining the conductance through \textit{time-independent} calculations alone. Applying the method to a Y-junction of interacting quantum wires, we numerically verify the theoretical prediction for the conductance of the chiral fixed-point of the Y-junction and then calculate the thus far unknown conductance of its M fixed point with time-independent density matrix renormalization group method.

cond-mat.mes-hall↗

arXiv2010

The Influence of Interference on the Kondo Effect in a Quantum Dot

We study the Kondo effect in a model system of a quantum dot embedded in an Aharanov-Bohm ring connected to two leads. By transforming to the scattering basis of the direct inter-lead tunneling, we are able to describe precisely how the Kondo screening of the dot spin occurs. We calculate the Kondo temperature and zero-temperature conductance and find that both are influenced by the Aharanov-Bohm ring as well as the electron density in the leads. We also calculate the form of an additional potential scattering term that arises at low energies due to the breaking of particle-hole symmetry. Many of our results are supported by numerical analysis using the numerical renormalization group.

cond-mat.mes-hall↗

arXiv2010

Interacting bosons in one dimension and Luttinger liquid theory

Harmonically trapped ultra-cold atoms and helium-4 in nanopores provide new experimental realizations of bosons in one dimension, motivating the search for a more complete theoretical understanding of their low energy properties. Worm algorithm path integral quantum Monte Carlo results for interacting bosons restricted to the one dimensional continuum are compared to the finite temperature and system size predictions of Luttinger liquid theory. For large system sizes at low temperature, excellent agreement is obtained after including the leading irrelevant interactions in the Hamiltonian which are determined explicitly.

cond-mat.stat-mech↗

arXiv2010

Tunable Luttinger liquid physics in biased bilayer graphene

Electronically gated bilayer graphene behaves as a tunable gap semiconductor under a uniform interlayer bias $V_{g}$. Imposing a spatially varying bias, which changes polarity from $-V_g$ to $+V_g$, leads to one dimensional (1D) chiral modes localized along the domain wall of the bias. Due to the broad transverse spread of their low-energy wavefunctions, we find that the dominant interaction between these 1D electrons is the forward scattering part of the Coulomb repulsion. Incorporating these interactions and the gate voltage dependence of the dispersion and wavefunctions, we find that these 1D modes behave as a strongly interacting Tomonaga-Luttinger liquid with three distinct mode velocities and a bias dependent Luttinger parameter, and discuss its experimental signatures.

cond-mat.str-el↗

arXiv2010

Interplay between Symmetric Exchange Anisotropy, Uniform Dzyaloshinskii-Moriya Interaction and Magnetic Fields in the Phase Diagram of Quantum Magnets and Superconductors

We theoretically study the joint influence of uniform Dzyaloshinskii-Moriya (DM) interactions, symmetric exchange anisotropy (with its axis parallel to the DM vector) and arbitrarily oriented magnetic fields on one-dimensional spin 1/2 antiferromagnets. We show that the zero-temperature phase diagram contains three competing phases: (i) an antiferromagnet with Neel vector in the plane spanned by the DM vector and the magnetic field, (ii) a {\em dimerized} antiferromagnet with Neel vector perpendicular to both the DM vector and the magnetic field, and (iii) a gapless Luttinger liquid. Phase (i) is destroyed by a small magnetic field component along the DM vector and is furthermore unstable beyond a critical value of easy-plane anisotropy, which we estimate using Abelian and non-Abelian bosonization along with perturbative renormalization group. We propose a mathematical equivalent of the spin model in a one-dimensional Josephson junction (JJ) array located in proximity to a bulk superconductor. We discuss the analogues of the magnetic phases in the superconducting context and comment on their experimental viability.

cond-mat.str-el↗

arXiv2010

The Kondo screening cloud: what it is and how to observe it

The Kondo effect involves the formation of a spin singlet by a magnetic impurity and conduction electrons. It is characterized by a low temperature scale, the Kondo temperature, $T_K$, and an associated long length scale, $ξ_K = \hbar v_F/(k_BT_K)$ where $v_F$ is the Fermi velocity. This Kondo length is often estimated theoretically to be in the range of .1 to 1 microns but such a long characteristic length scale has never been observed experimentally. In this review, I will examine how $ξ_K$ appears as a crossover scale when one probes either the dependence of physical quantities an distance from the impurity or when the impurity is embedded in a finite size structure and discuss possible experiments that might finally observe this elusive length scale.

cond-mat.mes-hall↗

arXiv2009

Quantum Impurity Problems in Condensed Matter Physics

Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to nanoscopic devices like quantum dots. In these lecture notes, I review this field, including the following topics: I. General Renormalization Group (RG) framework for quantum impurity problems: example of simplest Kondo model II. Multi-channel Kondo model III. Quantum Dots: experimental realizations of one and two channel Kondo models IV. Impurities in Luttinger liquids: point contact in a quantum wire V. Quantum impurity entanglement entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing operators and the X-ray edge problem.

cond-mat.str-el↗

arXiv2009

Entanglement entropy in quantum impurity systems and systems with boundaries

We review research on a number of situations where a quantum impurity or a physical boundary has an interesting effect on entanglement entropy. Our focus is mainly on impurity entanglement as it occurs in one dimensional systems with a single impurity or a boundary, in particular quantum spin models, but generalizations to higher dimensions are also reviewed. Recent advances in the understanding of impurity entanglement as it occurs in the spin-boson and Kondo impurity models are discussed along with the influence of boundaries. Particular attention is paid to 1+1 dimensional models where analytical results can be obtained for the case of conformally invariant boundary conditions and a connection to topological entanglement entropy is made. New results for the entanglement in systems with mixed boundary conditions are presented. Analytical results for the entanglement entropy obtained from Fermi liquid theory are also discussed as well as several different recent definitions of the impurity contribution to the entanglement entropy.

cond-mat.stat-mech↗

arXiv2009

Spectral function of spinless fermions on a one-dimensional lattice

We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is described by an effective x-ray edge type model. At low densities and for momentum near the zone boundary, we find a second divergent singularity at higher energies which is associated with a two-particle bound state. We use the Bethe ansatz solution of the model to calculate the exact singularity exponents for any momentum and for arbitrary values of chemical potential and interaction strength in the critical regime. We relate the singularities of the spectral function to the long-time decay of the fermion Green's function and compare our predictions with numerical results from the time-dependent density matrix renormalization group (tDMRG). Our results show that the tDMRG method is able to provide accurate time decay exponents in the cases of power-law decay of the Green's function. Some implications for the line shape of the dynamical structure factor away from half-filling are also discussed. In addition, the spectral weight of the Luttinger liquid result for the dynamical structure factor of the Heisenberg model at zero field is compared with the exact two-spinon contribution.

cond-mat.str-el↗