arXiv subjects

Ling-Yan Hung

Publications and source records attributed to Ling-Yan Hung.

At least 73 records · Page 4Linked to original sources

arXiv2014

Quantum quenches and competing orders: I. Time-dependent Hartree-Fock+BCS theory

We study the non-equlibrium dynamics of an electronic model of competing bond density wave order and $d$-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, $(\boldsymbol{k}, -\boldsymbol{k})$, in the Brillouin zone. We compare the results of numerical studies of our model with recent picosecond optical experiments.

cond-mat.supr-con↗

arXiv2014

Quantum quenches and competing orders

We study the nonequilibrium dynamics of an electronic model of competition between an unconventional charge density wave (a bond density wave) and $d$-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, ( $\boldsymbol{k}$, - $\boldsymbol{k}$ ), in the Brillouin zone. We also study the nonequilibrium dynamics of a quantum generalization of a O(6) nonlinear $σ$ model of competing orders in the underdoped cuprates [Hayward et al., Science $\boldsymbol{343}$, 1336 (2014)]. We obtain results, in the large $N$ limit of a O($N$) model, on the time dependence of correlation functions following a pulse disturbance. We compare our numerical studies with recent picosecond optical experiments. We find that, generically, the oscillatory responses in our models share various qualitative features with the experiments.

cond-mat.supr-con↗

arXiv2014

Universal symmetry-protected topological invariants for symmetry-protected topological states

Symmetry-protected topological (SPT) states are short-range entangled states with a symmetry G. They belong to a new class of quantum states of matter which are classified by the group cohomology $H^{d+1}(G,\mathbb{R}/\mathbb{Z})$ in d-dimensional space. In this paper, we propose a class of symmetry- protected topological invariants that may allow us to fully characterize SPT states with a symmetry group G (ie allow us to measure the cocycles in $H^{d+1}(G,\mathbb{R}/\mathbb{Z})$ that characterize the SPT states). We give an explicit and detailed construction of symmetry-protected topological invariants for 2+1D SPT states. Such a construction can be directly generalized to other dimensions.

cond-mat.str-el↗

arXiv2014

A Unified Framework of Topological Phases with Symmetry

In topological phases in $2+1$ dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work (arXiv:1308.4673), physics of a symmetry enriched phase can be extracted by the Mathematics of (hidden) quantum group symmetry breaking of a "parent phase". This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the $\text{Ising}\times\overline{\text{Ising}}$ phase breaks into the $\mathbb{Z}_2$ toric code with $\mathbb{Z}_2$ global symmetry; (2) the $SU(2)_8$ phase breaks into the chiral Fibonacci $\times$ Fibonacci phase with a $\mathbb{Z}_2$ symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge theory construction.

cond-mat.str-el↗

arXiv2013

Symmetry Enriched Phases via Pseudo Anyon Condensation

We show that a large class of symmetry enriched (topological) phases of matter in 2+1 dimensions can be embedded in "larger" topological phases- phases describable by larger hidden Hopf symmetries. Such an embedding is analogous to anyon condensation, although no physical condensation actually occurs. This generalizes the Landau-Ginzburg paradigm of symmetry breaking from continuous groups to quantum groups- in fact algebras- and offers a potential classification of the symmetry enriched (topological) phases thus obtained, including symmetry protected trivial phases as well, in a unified framework.

cond-mat.str-el↗

arXiv2013

(Non) supersymmetric quantum quenches

We explore supersymmetric quantum quenches of the mass and coupling constants in the $\mathcal{N}=1$ supersymmetric vector model using Hartee-Fock approximation. We find that in the case of the free fermionic field, quench of the mass generates singularity localized at the instant of sudden change and we point out the essential role of the parity of spacetime. Focusing on a supersymmetric generalization of the $ϕ^6$ model and using stationary phase approximation, we demonstrate that supersymmetry is broken in the asymptotic state that emerges at late times after the quench. Finally, we confirm SUSY breaking in the time-dependent setting by integrating numerically the exact equations of motion from the instant of the quench into asymptotic regime. We argue that the breaking of supersymmetry cannot be attributed to the thermal physics since to leading order in the Hartee-Fock approximation the final state is not thermal.

hep-th↗

arXiv2013

Relative Entropy and Holography

Relative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other, vanishing of relative entropy gives a powerful equation $ΔS=ΔH$ for the first order variation of the entanglement entropy $ΔS$ and the expectation value of the \modu Hamiltonian $ΔH$. We evaluate relative entropy between the vacuum and other states for spherical regions in the AdS/CFT framework. We check that the relevant equations and inequalities hold for a large class of states, giving a strong support to the holographic entropy formula. We elaborate on potential uses of the equation $ΔS=ΔH$ for vacuum state tomography and obtain modified versions of the Bekenstein bound.

hep-th↗

arXiv2013

Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases

We study the quantized topological terms in a weak-coupling gauge theory with gauge group $G_g$ and a global symmetry $G_s$ in $d$ space-time dimensions. We show that the quantized topological terms are classified by a pair $(G,ν_d)$, where $G$ is an extension of $G_s$ by $G_g$ and $ν_d$ an element in group cohomology $\cH^d(G,\R/\Z)$. When $d=3$ and/or when $G_g$ is finite, the weak-coupling gauge theories with quantized topological terms describe gapped symmetry enriched topological (SET) phases (i.e. gapped long-range entangled phases with symmetry). Thus, those SET phases are classified by $\cH^d(G,\R/\Z)$, where $G/G_g=G_s$. We also apply our theory to a simple case $G_s=G_g=Z_2$, which leads to 12 different SET phases in 2+1D, where quasiparticles have different patterns of fractional $G_s=Z_2$ quantum numbers and fractional statistics. If the weak-coupling gauge theories are gapless, then the different quantized topological terms may describe different gapless phases of the gauge theories with a symmetry $G_s$, which may lead to different fractionalizations of $G_s$ quantum numbers and different fractional statistics (if in 2+1D).

cond-mat.str-el↗

arXiv2013

A K matrix Construction of Symmetry Enriched Phases of Matter

We construct in the K matrix formalism concrete examples of symmetry enriched topological phases, namely intrinsically topological phases with global symmetries. We focus on the Abelian and non-chiral topological phases and demonstrate by our examples how the interplay between the global symmetry and the fusion algebra of the anyons of a topologically ordered system determines the existence of gapless edge modes protected by the symmetry and that a (quasi)-group structure can be defined among these phases. Our examples include phases that display charge fractionalization and more exotic non-local anyon exchange under global symmetry that correspond to general group extensions of the global symmetry group.

cond-mat.str-el↗

arXiv2012

String-Net Models with $Z_N$ Fusion Algebra

We study the Levin-Wen string-net model with a $Z_N$ type fusion algebra. Solutions of the local constraints of this model correspond to $Z_N$ gauge theory and double Chern-simons theories with quantum groups. For the first time, we explicitly construct a spin-$(N-1)/2$ model with $Z_N$ gauge symmetry on a triangular lattice as an exact dual model of the string-net model with a $Z_N$ type fusion algebra on a honeycomb lattice. This exact duality exists only when the spins are coupled to a $Z_N$ gauge field living on the links of the triangular lattice. The ungauged $Z_N$ lattice spin models are a class of quantum systems that bear symmetry-protected topological phases that may be classified by the third cohomology group $H^3(Z_N,U(1))$ of $Z_N$. Our results apply also to any case where the fusion algebra is identified with a finite group algebra or a quantusm group algebra.

cond-mat.other↗

arXiv2012

On c-theorems in arbitrary dimensions

The dilaton action in 3+1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the trace anomaly. Since there are no anomalies in odd dimensions, it is interesting to ask how such an action could arise otherwise. Motivated by this we use the AdS/CFT correspondence to examine both even and odd dimensional CFTs. We find that in even dimensions, by promoting the cut-off to a field, one can get an action for this field which coincides with the WZ action in flat space. In three dimensions, we observe that by finding an exact Hamilton-Jacobi counterterm, one can find a non-polynomial action which is invariant under global Weyl rescalings. We comment on how this finding is tied up with the F-theorem conjectures.

hep-th↗

arXiv2012

Quantized topological terms in weakly coupled gauge theories and their connection to symmetry protected topological phases

We consider a weakly coupled gauge theory where charged particles all have large gaps (ie no Higgs condensation to break the gauge "symmetry") and the field strength fluctuates only weakly. We ask what kind of topological terms can be added to the Lagrangian of such a weakly coupled gauge theory. In this paper, we systematically construct quantized topological terms which are generalization of the Chern-Simons terms and $F\wedge F$ terms, in space-time dimensions $d$ and for any gauge groups (continuous or discrete), using each element of the topological cohomology classes $H^{d+1}(BG,\Z)$ on the classifying space $BG$ of the gauge group $G$. In 3$d$ or for finite gauge groups above 3$d$, the weakly coupled gauge theories are gapped. So our results on topological terms can be viewed as a systematic construction of gapped topologically ordered phases of weakly coupled gauge theories. In other cases, the weakly coupled gauge theories are gapless. So our results can be viewed as an attempt to systematically construct different gapless phases of weakly coupled gauge theories. Amazingly, the bosonic symmetry protected topological (SPT) phases with a finite on-site symmetry group $G$ are also classified by the same $H^{d+1}(BG,\Z)$. (SPT phases are gapped quantum phases with a symmetry and trivial topological order.) In this paper, we show an explicit duality relation between topological gauge theories with the quantized topological terms and the bosonic SPT phases, for any finite group $G$ and in any dimensions; a result first obtained by Levin and Gu. We also study the relation between topological lattice gauge theory and the string-net states with non-trivial topological order and no symmetry.

cond-mat.str-el↗

arXiv2012

Modification of late time phase structure by quantum quenches

The consequences of the sudden change in the coupling constants (quenches) on the phase structure of the theory at late times are explored. We study in detail the three dimensional phi^6 model in the large N limit, and show that the phi^6 coupling enjoys a widened range of stability compared to the static scenario. Moreover, a new massive phase emerges, which for sufficiently large coupling becomes the dominant vacuum. We argue that these novel phenomena cannot be described by a simple thermalization effect or the emergence of a single effective temperature.

cond-mat.str-el↗

arXiv2012

On renormalization group flows and the a-theorem in 6d

We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p^6 in the low energy limit of n-point scattering amplitudes of the dilaton for n > 3. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p^6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4. Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.

hep-th↗

arXiv2011

On Holographic Entanglement Entropy and Higher Curvature Gravity

We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald's formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an alternate prescription which involves only the intrinsic curvature of the bulk surface. We verify that this prescription correctly reproduces the universal contribution to the entanglement entropy for CFT's in four and six dimensions. We also make further comments on gravitational theories with more general higher curvature interactions.

hep-th↗

arXiv2011

Some Calculable Contributions to Holographic Entanglement Entropy

Using the AdS/CFT correspondence, we examine entanglement entropy for a boundary theory deformed by a relevant operator and establish two results. The first is that if there is a contribution which is logarithmic in the UV cut-off, then the coefficient of this term is independent of the state of the boundary theory. In fact, the same is true of all of the coefficients of contributions which diverge as some power of the UV cut-off. Secondly, we show that the relevant deformation introduces new logarithmic contributions to the entanglement entropy. The form of some of these new contributions is similar to that found recently in an investigation of entanglement entropy in a free massive scalar field theory [1].

hep-th↗

arXiv2010

String Junctions and Holographic Interfaces

In this paper we study half-BPS type IIB supergravity solutions with multiple $AdS_3\times S^3\times M_4$ asymptotic regions, where $M_4$ is either $T^4$ or $K_3$. These solutions were first constructed in [1] and have geometries given by the warped product of $AdS_2 \times S^2 \times M_4 $ over $Σ$, where $Σ$ is a Riemann surface. We show that the holographic boundary has the structure of a star graph, i.e. $n$ half-lines joined at a point. The attractor mechanism and the relation of the solutions to junctions of self-dual strings in six-dimensional supergravity are discussed. The solutions of [1] are constructed introducing two meromorphic and two harmonic functions defined on $Σ$. We focus our analysis on solutions corresponding to junctions of three different conformal field theories and show that the conditions for having a solution charged only under Ramond-Ramond three-form fields reduce to relations involving the positions of the poles and the residues of the relevant harmonic and meromorphic functions. The degeneration limit in which some of the poles collide is analyzed in detail. Finally, we calculate the holographic boundary entropy for a junction of three CFTs and obtain a simple expression in terms of poles and residues.

hep-th↗

arXiv2010

On 1-loop diagrams in AdS space and the random disorder problem

We study the complex scalar loop corrections to the boundary-boundary gauge two point function in pure AdS space in Poincare coordinates, in the presence of a boundary quadratic perturbation to the scalar. These perturbations correspond to double trace perturbations in the dual CFT and modify the boundary conditions of the bulk scalars in AdS. We find that, in addition to the usual UV divergences, the 1-loop calculation suffers from a divergence originating in the limit as the loop vertices approach the AdS horizon. We show that this type of divergence is independent of the boundary coupling, and making use of which we extract the finite relative variation of the imaginary part of the loop via Cutkosky rules as the boundary perturbation varies. Applying our methods to compute the effects of a time-dependent impurity to the conductivities using the replica trick in AdS/CFT, we find that generally an IR-relevant disorder reduces the conductivity and that in the extreme low frequency limit the correction due to the impurities overwhelms the planar CFT result even though it is supposedly $1/N^2$ suppressed. Comments on the effect of time-independent impurity in such a system are presented.

hep-th↗