arXiv subjects

Ian Affleck

Publications and source records attributed to Ian Affleck.

At least 19 recordsLinked to original sources

arXiv2026

Soliton-antisoliton pairs in the supersymmetric gapped phase of an interacting Majorana chain

A strongly interacting chain of Majorana fermions realizes the supersymmetric tricritical Ising phase, with supersymmetry (SUSY) extending into a symmetry-broken ordered phase adjacent to the tricritical point. Although the signatures of SUSY at the tricritical point are well understood, their behavior in the gapped phase remains less clear. Here, we address two key questions: how SUSY manifests in the gapped phase and what is the nature of the excitations in this phase. We show that, in the thermodynamic limit, a conventional SUSY diagnostic that remains finite at the tricritical point diverges immediately on the Ising side, yet decays continuously to zero deeper in the gapped phase, signaling the persistence of SUSY. Focusing on the lowest excited states in the supersymmetric gapped regime, we find that the excitations consist of soliton-antisoliton pairs separating distinct ordered regions. Each soliton binds an emergent localized Majorana mode, and together the pair forms a nonlocal Dirac fermion. The occupation of this Dirac mode distinguishes eigenstates with even and odd fermion parity.

cond-mat.str-el↗

arXiv2024

Left-left-right-right magnetic order in spin-1/2 Kitaev-Heisenberg chain

In this work, we perform a combination of analytical and numerical studies on the phase diagram of the spin-1/2 Kitaev-Heisenberg chain in the region of negative Kitaev and positive Heisenberg couplings. Apart from the antiferromagnetic phase, we find a magnetically ordered phase with left-left-right-right order and a gapless phase with central charge value $c=1$, resolving the existing contradictory results in literature regarding this parameter region. In particular, the origin of the left-left-right-right order is clarified based on a perturbative Luttinger liquid analysis. The left-left-right-right phase is further shown to persist in the Kitaev-Heisenberg-Gamma model when a small nonzero Gamma interaction is introduced. Using a coupled-chain method, we also demonstrate that the one-dimensional (1D) left-left-right-right order gives a quasi-1D explanation for the 2D stripy order of the same model on the honeycomb lattice.

cond-mat.str-el↗

arXiv2022

Nonsymmorphic spin-space cubic groups and SU(2)$_1$ conformal invariance in one-dimensional spin-1/2 models

Recently, extended gapless phases with emergent SU(2)$_1$ conformal invariance occupying finite regions in the phase diagrams have been found in one-dimensional spin-1/2 models with nonsymmorphic $O_h$ symmetry groups. In this work, we investigate the question of whether the conditions for emergent SU(2)$_1$ invariance can be loosened. We find that besides the nonsymmorphic $O_h$ group, the other four smaller nonsymmorphic cubic groups including $O$, $T_h$, $T_d$ and $T$ can also give rise to emergent SU(2)$_1$ invariance. Minimal spin-1/2 models having these nonsymmorphic cubic groups as symmetry groups are constructed, and numerical evidences for the emergent SU(2)$_1$ invariance are provided. Our work is useful for understanding gapless phases in one-dimensional spin systems with nonsymmorphic symmetries.

cond-mat.str-el↗

arXiv2022

Counter-rotating spiral, zigzag, and 120$^\circ$ orders from coupled-chain analysis of Kitaev-Gamma-Heisenberg model, and relations to honeycomb iridates

We study the nearest neighboring spin-1/2 Kitaev-Heisenberg-Gamma ($KJ\Gamma$) model on the honeycomb lattice in the parameter region of ferromagnetic (FM) Kitaev and antiferromagnetic (AFM) Heisenberg couplings relevant for honeycomb iridates, using a coupled-chain analysis. Starting from the gapless Luttinger liquid phase of a decoupled $KJ\Gamma$ chain, the inter-chain interactions in the two-dimensional model is treated within a self-consistent mean field approach based on the Luttinger liquid theory. In the FM Gamma region, our analysis recovers the reported 120$^\circ$ magnetic order, previously obtained by classical analysis and exact diagonalization method. On the other hand, new physics is revealed in the AFM Gamma region, where three magnetic orders are found, including 120$^\circ$, commensurate counter-rotating spiral, and zigzag orders. Interestingly, the two first order phase transition lines separating these three magnetic orders merge at a single point at $K = -2 \Gamma$ and $J=0$, which is predicted to be a quantum critical point. The current theory captures the experimentally observed counter-rotating spiral order in $\alpha$-Li$_22$IrO$_3$ and the zigzag order in Na$_2$IrO$_3$, thereby indicating that the spin-1/2 $KJ\Gamma$ model may serve as a minimal model for honeycomb iridates. Limitations of the mean field theory presented in this work and the $J \rightarrow 0$ regime are also discussed.

cond-mat.str-el↗

arXiv2022

Emergent SU(2)$_1$ conformal symmetry in the spin-1/2 Kitaev-Gamma chain with a Dzyaloshinskii-Moriya interaction

We study the one-dimensional spin-1/2 Kitaev-Gamma model with a bond-dependent Dzyaloshinskii-Moriya (DM) interaction, which can be induced by an electric field applied in the third direction where the first and second directions refer to the two bond directions in the model. By a combination of field theory and symmetry analysis, an extended gapless phase with an emergent SU(2)$_1$ conformal symmetry is found in the phase diagram of the spin-1/2 Kitaev-Gamma-DM chain. The analytic predictions are in good agreements with numerical results obtained from density matrix renormalization group simulations.

cond-mat.str-el↗

arXiv2022

Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin-$\frac{1}{2}$ chains from a renormalization-group perspective

Recently, in the Luttinger liquid phase of the one-dimensional generalized antiferromagnetic Kitaev spin-1/2 model, it has been found that the abelian bosonization formulas of the local spin operators only respect the exact discrete nonsymmorphic symmetry group of the model, not the emergent U(1) symmetry. In this work, we perform a renormalization group (RG) study to provide explanations for the origin of the U(1) breaking terms in the bosonization formulas. We find that the lack of U(1) symmetry originates from the wavefunction renormalization effects in the spin operators along the RG flow induced by the U(1) breaking interactions in the microscopic Hamiltonian. In addition, the RG analysis can give predictions to the signs and order of magnitudes of the coefficients in the bosonization formulas. Our work is helpful to understand the rich nonsymmorphic physics in one-dimensional Kitaev spin models.

cond-mat.str-el↗

arXiv2022

Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models

In this work, we perform a detailed study on the consequences of nonsymmorphic symmetries in the Luttinger phase of the one-dimensional spin-1/2 Kitaev-Heisenberg-Gamma model with an antiferromagnetic Kitaev interaction. Nonsymmorphic bosonization formulas for the spin operators are proposed, containing ten non-universal coefficients which are determined by our density matrix renormalization group simulations to a high degree of accuracy. Using the nonsymmorphic bosonization formulas, different Fourier components and decay powers in the correlation functions are disentangled, the response to weak magnetic fields is analyzed, and the zigzag magnetic order in two dimensions is recovered from a system of weakly coupled chains. We also find a line of critical points with an emergent SU(2)$_1$ conformal symmetry located on the boundary of the Luttinger liquid phase, where a nonabelian version of nonsymmorphic bosonization should be applied.

cond-mat.str-el↗

arXiv2022

From SU(2)$_5$ to SU(2)$_3$ Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain

We investigate the properties of a frustrated spin-5/2 chain with next-nearest neighbor two and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possible presence of a critical floating phase at intermediate values of the next-nearest neighbor interaction. We provide strong evidence that the continuous transition into the dimerized phase, which has been found to be generically in the Wess-Zumino-Witten SU(2)$_{2S}$ universality class up to spin $S=2$, is SU(2)$_5$ only at two isolated points of the phase diagram, and that it is SU(2)$_3$ in between, in agreement with the presence of two relevant operators allowed by symmetry for SU(2)$_5$, and with the conservation of the parity of the level index along the renormalization flow between SU(2)$_k$ theories with different values of $k$. We also find that the dimerization induced by the next-nearest neighbor interaction is a three step process, with first a small partially dimerized phase followed by a broad critical floating phase with incommensurate correlations before the fully dimerized phase is reached. Implications for the iron oxide ${\mathrm{Bi}}_{3}{\mathrm{FeMo}}_{2}{\mathrm{O}}_{12}$ are briefly discussed.

cond-mat.str-el↗

arXiv2022

Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation

Affleck, Kennedy, Lieb, and Tasaki constructed a spin-1 model that is isotropic in spins and possesses a provable finite gap above the ground state more than three decades ago. They also constructed models in two dimensions. Their construction has impacted subsequent research that is still active. In this review article, we review some selected the progresses, such as magnetic ordering of the AKLT models, emerging phases under deforming the AKLT Hamiltonians, symmetry-protected topological order in several AKLT models, their spectral gap, and applications for quantum computation.

cond-mat.str-el↗

arXiv2022

Symmetry analysis of bond-alternating Kitaev spin chains and ladders

In this work, we analyze the nonsymmorphic symmetry group structures for a variety of generalized Kitaev spin chains and ladders with bond alternations, including Kitaev-Gamma chain, Kitaev-Heisenberg-Gamma chain, beyond nearest neighbor interactions, and two-leg spin ladders. The symmetry analysis is applied to determine the symmetry breaking patterns of several magnetically ordered phases in the bond-alternating Kitaev-Gamma spin chains, as well as the dimerization order parameters for spontaneous dimerizations. Our work is useful in understanding the magnetic phases in related models and may provide guidance for the symmetry classifications of mean field solutions in further investigations.

cond-mat.str-el↗

arXiv2021

Multi-impurity chiral Kondo model: correlation functions and anyon fusion rules

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity-spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the inter-impurity spin correlation probes the anyon fusion of the pair of correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid the multichannel Kondo anyons via consecutive measurements.

cond-mat.str-el↗

arXiv2021

The case of SU$(3)$ criticality in spin-2 chains

It was proposed in [(https://doi.org/10.1103/PhysRevLett.114.145301){Chen et al., Phys. Rev. Lett. $\mathbf{114}$, 145301 (2015)}] that spin-2 chains display an extended critical phase with enhanced SU$(3)$ symmetry. This hypothesis is highly unexpected for a spin-2 system and, as we argue, would imply an unconventional mechanism for symmetry emergence. Yet, the absence of convenient critical points for renormalization group perturbative expansions, allied with the usual difficulty in the convergence of numerical methods in critical or small-gapped phases, renders the verification of this hypothetical SU$(3)$-symmetric phase a non-trivial matter. By tracing parallels with the well-understood phase diagram of spin-1 chains and searching for signatures robust against finite-size effects, we draw criticism on the existence of this phase. We perform non-Abelian density matrix renormalization group studies of multipolar static correlation function, energy spectrum scaling, single-mode approximation, and entanglement spectrum to shed light on the problem. We determine that the hypothetical SU$(3)$ spin-2 phase is, in fact, dominated by ferro-octupolar correlations and also observe a lack of Luttinger-liquid-like behavior in correlation functions that suggests that is perhaps not critical. We further construct an infinite family of spin-$S$ systems with similar ferro-octupolar-dominated quasi-SU$(3)$-like phenomenology; curiously, we note that the spin-3 version of the problem is located in a subspace of exact G$_2$ symmetry, making this a point of interest for search of Fibonacci topological properties in magnetic systems.

cond-mat.str-el↗

arXiv2021

SO(5) critical point in a spin-flavor Kondo device -- Bosonization and refermionization solution

We investigate a well studied system of a quantum dot coupled to a Coulomb box and leads, realizing a spin-flavor Kondo model. It exhibits a recently discovered non-Fermi liquid (NFL) behavior with emergent SO(5) symmetry. Here, through a detailed bosonization and refermionization solution, we push forward our previous work and provide a consistent and complete description of the various exotic properties and phase diagram. A unique NFL phase emerges from the presence of an uncoupled Majorana fermion from the flavor sector, whereas FL-like susceptibilities result from the gapping out of a pair of Majroana fermions from the spin and flavor sectors. Other properties, such as a $T^{3/2}$ scaling of the conductance, stability under channel or spin symmetry breaking and a re-appearance of NFL behavior upon breaking the particle-hole symmetry, are all accounted for by a renormalization group treatment of the refermionized Majorana model.

cond-mat.str-el↗

arXiv2021

Flag manifold sigma models: spin chains and integrable theories

This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin chains, and their phase structure is sensitive to the values of the topological angles, which are determined by the representations of spins in the chain. Gapless phases can in certain cases be explained by the presence of discrete 't Hooft anomalies in the continuum theory. We also discuss integrable flag manifold sigma models, which provide a generalization of the theory of integrable models with symmetric target spaces. These models, as well as their deformations, have an alternative equivalent formulation as bosonic Gross-Neveu models, which proves useful for demonstrating that the deformed geometries are solutions of the renormalization group (Ricci flow) equations, as well as for the analysis of anomalies and for describing potential couplings to fermions.

hep-th↗

arXiv2020

SO(5) non-Fermi liquid in a Coulomb box device

Non-Fermi liquid (NFL) physics can be realized in quantum dot devices where competing interactions frustrate the exact screening of dot spin or charge degrees of freedom. We show that a standard nanodevice architecture, involving a dot coupled to both a quantum box and metallic leads, can host an exotic SO(5) symmetry Kondo effect, with entangled dot and box charge and spin. This NFL state is surprisingly robust to breaking channel and spin symmetry, but destabilized by particle-hole asymmetry. By tuning gate voltages, the SO(5) state evolves continuously to a spin and then "flavor" two-channel Kondo state. The expected experimental conductance signatures are highlighted.

cond-mat.str-el↗

arXiv2020

A shell model for superfluids in rough-walled nanopores

Recent experiments on the flow of helium-4 fluid through nanopores with tunable pore radius provide a platform for studying the quasi-one-dimensional (quasi-1D) superfluid behaviors. In the extreme 1D limit, the helium atoms are localized by disordered small variations in the substrate potential provided by the pore walls. In the limit of wide pore radius, a solid layer of helium-4 is expected to coat the pore walls smoothing out the substrate potential, and superfluidity is observed in the central region. Building on earlier quantum Monte Carlo results, we propose a scenario for this crossover using a shell model of coupled Luttinger liquids. We find that a small radius pore will always localize the helium atoms, but above a critical radius, a single 1D channel flows through the pore and can be described by Luttinger liquid theory.

cond-mat.mes-hall↗

arXiv2020

Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus

Majorana modes can arise as zero energy bound states in a variety of solid state systems. A two-dimensional phase supporting these quasiparticles, for instance, emerges on the surface of a topological superconductor with the zero modes localized at the cores of vortices. At low energies, such a setup can be modeled by Majorana modes that interact with each other on the Abrikosov lattice. In experiments, the lattice is usually triangular. Motivated by the practical relevance, we explore the phase diagram of this Hubbard-like Majorana model using a combination of mean field theory and numerical simulation of thin torus geometries through the density matrix renormalization group algorithm. Our analysis indicates that attractive interactions between Majoranas can drive a phase transition in an otherwise gapped topological state.

cond-mat.str-el↗

arXiv2020

Spin wave theory of one-dimensional generalized Kitaev model

In this work, we perform a combination of classical and spin wave analysis on the one-dimensional spin-$S$ Kitaev-Heisenberg-Gamma model in the region of an antiferromagnetic Kitaev coupling. Four phases are found, including a N\'eel ordered phase, a phase with $O_h\rightarrow D_3$ symmetry breaking, and "$D_3$-breaking I, II" phases which both break $D_3$ symmetries albeit in different ways, where $O_h$ is the full octahedral group and $D_3$ is the dihedral group of order six. The lowest-lying spin wave mass is calculated perturbatively in the vicinity of the hidden SU(2) symmetric ferromagnetic point.

cond-mat.str-el↗