arXiv subjects

Chien-Hung Lin

Publications and source records attributed to Chien-Hung Lin.

18 recordsLinked to original sources

arXiv2023

Anyon condensation in the string-net models

We study condensation of abelian bosons in string-net models, by constructing a family of Hamiltonians that can be tuned through any such transition. We show that these Hamiltonians admit two exactly solvable, string-net limits: one deep in the uncondensed phase, described by an initial, uncondensed string net Hamiltonian, and one deep in the condensed phase, described by a final, condensed string net model. We give a systematic description of the condensed string net model in terms of the uncondensed string net and the data associated with the condensing abelian bosons. Specifically, if the uncondensed string net is described by a fusion category $\mathcal{C}$, we show how the string labels and fusion data of the fusion category $\mathcal{\tilde{C}}$ describing the condensed string net can be obtained from that of $\mathcal{C}$ and the data describing the string oeprators that create the condensing boson. This construction generalizes previous approaches to anyon condensation in string nets, by allowing the condensation of arbitrary abelian bosons, including chiral bosons in string nets constructed from (for example) Chern-Simons theories, which describe time-reversal invariant bilayer states. This gives a method for obtaining the full data for string nets without explicit time-reversal symmetry from such bilayer models. We illustrate our approach with several examples.

cond-mat.str-el↗

arXiv2022

Continuous transition between Ising magnetic order and a chiral spin liquid

The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian $SO(N)$ gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to $\mathbb{Z}_2$ monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.

cond-mat.str-el↗

arXiv2020

Generalized string-net models: A thorough exposition

We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter. The ground states of these models can be thought of as superpositions of different "string-net configurations", where each string-net configuration is a trivalent graph with labeled edges, drawn in the $xy$ plane. What makes this construction more general than the original string-net construction is that, unlike the original construction, tetrahedral reflection symmetry is not assumed, nor is it assumed that the ground state wave function $\Phi$ is "isotropic": i.e. in the generalized setup, two string-net configurations $X_1, X_2$ that can be continuously deformed into one another can have different ground state amplitudes, $\Phi(X_1) \neq \Phi(X_2)$. As a result, generalized string-net models can realize topological phases that are inaccessible to the original construction. In this paper, we provide a more detailed discussion of ground state wave functions, Hamiltonians, and minimal self-consistency conditions for generalized string-net models than what exists in the previous literature. We also show how to construct string operators that create anyon excitations in these models, and we show how to compute the braiding statistics of these excitations. Finally, we derive necessary and sufficient conditions for generalized string-net models to have isotropic ground state wave functions on the plane or the sphere -- a property that may be useful in some applications.

cond-mat.str-el↗

arXiv2018

Transition between algebraic and $\mathbb{Z}_2$ quantum spin liquids at large $N$

We present a field theory description of a quantum phase transition in two spatial dimensions between a $U(1)$ algebraic spin liquid with $N$ flavors of gapless two-component Dirac fermionic spinons and a gapped $\mathbb{Z}_2$ spin liquid. This transition is driven by spinon pairing and concomitant Higgsing of the emergent $U(1)$ gauge field. For sufficiently large $N$ we find a quantum critical point with non-Gaussian exponents that is stable against instanton proliferation. We compute critical exponents using either $1/N$ or $\epsilon$ expansions, and give estimates of the critical value of $N$ below which the quantum critical point disappears.

cond-mat.str-el↗

arXiv2016

Multi-flavor string-net models

We generalize the string-net construction to multiple flavors of strings, each of which is labeled by the elements of an abelian group $G_i$. The same flavor of strings can branch while different flavors of strings can cross one another and thus they form intersecting string-nets. We systematically construct the exactly soluble lattice Hamiltonians and the ground state wave functions for the intersecting string-net condensed phases. We analyze the braiding statistics of the low energy quasiparticle excitations and find that our model can realize all the topological phases as the string-net model with group $G=\prod_i G_i$. In this respect, our construction suggests several ways of building lattice models which realize topological order $G$. They correspond to intersecting string-net models with various choices of flavors of strings associated with different decomposition of $G$. In fact, our construction concretely demonstrates the K\text{\"u}nneth formula by constructing various lattice models with the same topological order. As an example, we construct the $G=\mathbb{Z}_2\times \mathbb{Z}_2 \times \mathbb{Z}_2 $ string-net model which realizes a non-abelian topological phase by properly intersecting three copies of toric codes.

cond-mat.str-el↗

arXiv2016

Superconducting quantum criticality of topological surface states at three loops

The semimetal-superconductor quantum phase transition on the two-dimensional (2D) surface of a 3D topological insulator is conjectured to exhibit an emergent $\mathcal{N}=2$ supersymmetry, based on a renormalization group (RG) analysis at one-loop order in the $ε$ expansion. We provide additional support for this conjecture by performing a three-loop RG analysis and showing that the supersymmetric fixed point found at this order survives the extrapolation to 2D. We compute critical exponents to order $ε^3$, obtaining the more accurate value $ν\approx 0.985$ for the correlation length exponent and confirming that the fermion and boson anomalous dimensions remain unchanged beyond one loop, as expected from non-renormalization theorems in supersymmetric theories. We further couple the system to a dynamical $U(1)$ gauge field, and argue that the transition becomes fluctuation-induced first order. We discuss implications of this result for quantum phase transitions between certain symmetry-preserving correlated surface states of 3D topological insulators.

cond-mat.str-el↗

arXiv2016

Interacting fermionic symmetry-protected topological phases in two dimensions

We classify and construct models for two-dimensional (2D) interacting fermionic symmetry-protected topological (FSPT) phases with general finite Abelian unitary symmetry $G_f$. To obtain the classification, we couple the FSPT system to a dynamical discrete gauge field with gauge group $G_f$ and study braiding statistics in the resulting gauge theory. Under reasonable assumptions, the braiding statistics data allows us to infer a potentially complete classification of 2D FSPT phases with Abelian symmetry. The FSPT models that we construct are simple stacks of the following two kinds of existing models: (i) free-fermion models and (ii) models obtained through embedding of bosonic symmetry-protected topological (BSPT) phases. Interestingly, using these two kinds of models, we are able to realize almost all FSPT phases in our classification, except for one class. We argue that this exceptional class of FSPT phases can never be realized through models (i) and (ii), and therefore can be thought of as intrinsically interacting and intrinsically fermionic. The simplest example of this class is associated with $\mathbb Z_4^f\times\mathbb Z_4\times\mathbb Z_4$ symmetry. We show that all 2D FSPT phases with a finite Abelian symmetry of the form $ \mathbb Z_2^f\times G$ can be realized through the above models (i), or (ii), or a simple stack of them. Finally, we study the stability of BSPT phases when they are embedded into fermionic systems.

cond-mat.str-el↗

arXiv2016

Emergence of supersymmetric quantum electrodynamics

Supersymmetric (SUSY) gauge theories such as the Minimal Supersymmetric Standard Model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator (TI) hosting three Dirac cones, such as the topological Kondo insulator SmB$_6$. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric XYZ model, which is dual by mirror symmetry to $\mathcal{N}=2$ supersymmetric quantum electrodynamics (SQED) in 2+1 dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine exactly certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point, which may be measured in future experiments.

cond-mat.str-el↗

arXiv2015

Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases

We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological (SPT) phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data is defined in terms of the statistics of bulk excitations, while the surface data is defined in terms of the statistics of surface excitations. An appealing property of this data is that it is plausibly complete in the sense that the bulk data uniquely distinguishes each 3D SPT phase, while the surface data uniquely distinguishes each gapped, symmetric surface. Our correspondence applies to any 3D bosonic SPT phase with finite Abelian unitary symmetry group. It applies to any surface that (1) supports only Abelian anyons and (2) has the property that the anyons are not permuted by the symmetries.

cond-mat.str-el↗

arXiv2015

Loop braiding statistics in exactly soluble 3D lattice models

We construct two exactly soluble lattice spin models that demonstrate the importance of three-loop braiding statistics for the classification of 3D gapped quantum phases. The two models are superficially similar: both are gapped and both support particle-like and loop-like excitations similar to that of charges and vortex lines in a $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge theory. Furthermore, in both models the particle excitations are bosons, and in both models the particle and loop excitations have the same mutual braiding statistics. The difference between the two models is only apparent when one considers the recently proposed three-loop braiding process in which one loop is braided around another while both are linked to a third loop. We find that the statistical phase associated with this process is different in the two models, thus proving that they belong to two distinct phases. An important feature of this work is that we derive our results using a concrete approach: we construct string and membrane operators that create and move the particle and loop excitations and then we extract the braiding statistics from the commutation algebra of these operators.

cond-mat.str-el↗

arXiv2014

Generalizations and limitations of string-net models

We ask which topological phases can and cannot be realized by exactly soluble string-net models. We answer this question for the simplest class of topological phases, namely those with abelian braiding statistics. Specifically, we find that an abelian topological phase can be realized by a string-net model if and only if (i) it has a vanishing thermal Hall conductance and (ii) it has at least one Lagrangian subgroup --- a subset of quasiparticles with particular topological properties. Equivalently, we find that an abelian topological phase is realizable if and only if it supports a gapped edge. We conjecture that the latter criterion generalizes to the non-abelian case. We establish these results by systematically constructing all possible abelian string-net models and analyzing the quasiparticle braiding statistics in each model. We show that the low energy effective field theories for these models are multicomponent U(1) Chern-Simons theories, and we derive the K-matrix description of each model. An additional feature of this work is that the models we construct are more general than the original string-net models, due to several new ingredients. First, we introduce two new objects $γ, α$ into the construction which are related to $\mathbb{Z}_2$ and $\mathbb{Z}_3$ Frobenius-Schur indicators. Second, we do not assume parity invariance. As a result, we can realize topological phases that were not accessible to the original construction, including phases that break time-reversal and parity symmetry.

cond-mat.str-el↗

arXiv2012

Zero bias conductance peak in Majorana wires made of semiconductor-superconductor hybrid structures

Motivated by a recent experimental report[1] claiming the likely observation of the Majorana mode in a semiconductor-superconductor hybrid structure[2,3,4,5], we study theoretically the dependence of the zero bias conductance peak associated with the zero-energy Majorana mode in the topological superconducting phase as a function of temperature, tunnel barrier potential, and a magnetic field tilted from the direction of the wire for realistic wires of finite lengths. We find that higher temperatures and tunnel barriers as well as a large magnetic field in the direction transverse to the wire length could very strongly suppress the zero-bias conductance peak as observed in Ref.[1]. We also show that a strong magnetic field along the wire could eventually lead to the splitting of the zero bias peak into a doublet with the doublet energy splitting oscillating as a function of increasing magnetic field. Our results based on the standard theory of topological superconductivity in a semiconductor hybrid structure in the presence of proximity-induced superconductivity, spin-orbit coupling, and Zeeman splitting show that the recently reported experimental data are generally consistent with the existing theory that led to the predictions for the existence of the Majorana modes in the semiconductor hybrid structures in spite of some apparent anomalies in the experimental observations at first sight. We also make several concrete new predictions for future observations regarding Majorana splitting in finite wires used in the experiments.

cond-mat.mes-hall↗

arXiv2012

Quantum Dynamics of Disordered Bosons in an Optical Lattice

We study the equilibrium and non-equilibrium properties of strongly interacting bosons on a lattice in presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase diagram of the disordered Bose Hubbard model and obtain the Mott insulator, Bose glass and superfluid phases. We also study the non equilibrium response of the system under a periodic temporal drive where, starting from the superfluid phase, the hopping parameter is ramped down linearly in time, and back to its initial value. We study the density of excitations created, the change in the superfluid order parameter and the energy pumped into the system in this process as a function of the inverse ramp rate $τ$. For the clean case the density of excitations goes to a constant, while the order parameter and energy relaxes as $1/τ$ and $1/τ^2$ respectively. With disorder, the excitation density decays exponentially with $τ$, with the decay rate increasing with the disorder, to an asymptotic value independent of the disorder. The energy and change in order parameter also decrease as $τ$ is increased.

cond-mat.quant-gas↗

arXiv2011

Low-density molecular gas of tightly-bound Rashba-Dresselhaus fermions

We study interacting Rashba-Dresselhaus fermions in two spatial dimensions. First, we present a new exact solution to the two-particle pairing problem of spin-orbit-coupled fermions for arbitrary Rashba and Dresselhaus spin-orbit interactions. An exact molecular wave function and the Green function are explicitly derived along with the binding energy and the spectrum of the molecular state. In the second part, we consider a thermal Boltzmann gas of fermionic molecules and compute the time-of-flight velocity and spin distributions for a single fermion in the gas. We show that the pairing signatures can be observed already in the first-moment expectation values, such as time-of-flight density and spin profiles.

cond-mat.quant-gas↗

arXiv2010

Quantum rotor theory of spinor condensates in tight traps

In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensates. In a previous work it was shown that there is an exact mapping of a spin-one condensate of fixed particle number with quadratic Zeeman interaction onto a quantum rotor model. Since the rotor model has an unbounded spectrum from above, it has many more eigenstates than the original bosonic model. Here we show that for each subset of states with fixed spin F_z, the physical rotor eigenstates are always those with lowest energy. We classify three distinct physical limits of the rotor model: the Rabi, Josephson, and Fock regimes. The last regime corresponds to a fragmented condensate and is thus not captured by the Bogoliubov theory. We next consider the semiclassical limit of the rotor problem and make connections with the quantum wave functions through use of the Husimi distribution function. Finally, we describe how to extend the analysis to higher-spin systems and derive a rotor model for the spin-two condensate. Theoretical details of the rotor mapping are also provided here.

cond-mat.quant-gas↗

arXiv2010

Interaction induced ferro-electricity in the rotational states of polar molecules

We show that a ferro-electric quantum phase transition can be driven by the dipolar interaction of polar molecules in the presence a micro-wave field. The obtained ferro-electricity crucially depends on the harmonic confinement potential, and the resulting dipole moment persists even when the external field is turned off adiabatically. The transition is shown to be second order for fermions and for bosons of a smaller permanent dipole moment, but is first order for bosons of a larger moment. Our results suggest the possibility of manipulating the microscopic rotational state of polar molecules by tuning the trap's aspect ratio (and other mesoscopic parameters), even though the later's energy scale is smaller than the former's by six orders of magnitude.

cond-mat.quant-gas↗

arXiv2008

Nanomechanical-resonator-assisted induced transparency in a Cooper-pair-box system

We propose a scheme to demonstrate the electromagnetically induced transparency (EIT) in a system of a superconducting Cooper-pair box coupled to a nanomechanical resonator. In this scheme, the nanomechanical resonator plays an important role to contribute additional auxiliary energy levels to the Cooper-pair box so that the EIT phenomenon could be realized in such a system. We call it here resonator-assisted induced transparency (RAIT). This RAIT technique provides a detection scheme in a real experiment to measure physical properties, such as the vibration frequency and the decay rate, of the coupled nanomechanical resonator.

cond-mat.supr-con↗

arXiv2006

Systematic {\em ab initio} study of the phase diagram of epitaxially strained SrTiO$_3$

We use density-functional theory with the local-density approximation to study the structural and ferroelectric properties of SrTiO$_3$ under misfit strains. Both the antiferrodistortive (AFD) and ferroelectric (FE) instabilities are considered. The rotation of the oxygen octahedra and the movement of the atoms are fully relaxed within the constraint of a fixed in-plane lattice constant. We find a rich misfit strain-induced phase transition sequence and is obtained only when the AFD distortion is taken into account. We also find that compressive misfit strains induce ferroelectricity in the tetragonal low temperature phase only whilst tensile strains induce ferroelectricity in the orthorhombic phases only. The calculated FE polarization for both the tetragonal and orthorhombic phases increases monotonically with the magnitude of the strains. The AFD rotation angle of the oxygen octahedra in the tetragonal phase increases dramatically as the misfit strain goes from the tensile to compressive strain region whilst it decreases slightly in the orthorhombic (FO4) phase. This reveals why the polarization in the epitaxially strained SrTiO$_3$ would be larger when the tensile strain is applied, since the AFD distortion is found to reduce the FE instability and even to completely suppress it in the small strain region. Finally, our analysis of the average polar distortion and the charge density distribution suggests that both the Ti-O and Sr-O layers contribute significantly to the FE polarization.

cond-mat.mtrl-sci↗