arXiv subjects

Ömer M. Aksoy

Publications and source records attributed to Ömer M. Aksoy.

18 recordsLinked to original sources

arXiv2026

Competing symmetry breaking and topology in quantum spin chains

We investigate how spontaneous symmetry breaking and symmetry-protected topology compete and cooperate in one-dimensional quantum spin-1/2 systems. We introduce two families of local Hamiltonians with $\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{T}_{2}$ symmetry which host a zoo of broken-symmetry phases with and without gapless boundary spins, namely, six long-range-ordered gapped phases that differ by their $\mathbb{Z}^{\,}_{2}$-symmetry-breaking patterns (FM$^{\,}_{x,y,z}$ and Neel$^{\,}_{x,y,z}$), their partner symmetry-protected topological phases (FM$^{\mathrm{SPT}}_{x,y}$ and Neel$^{\mathrm{SPT}}_{x,y}$), and two gapless phases (gFM$^{\,}_{z}$ and gNeel$^{\,}_{z}$) with incommensurate $\mathbb{Z}^{T}_{2}$-breaking magnetic long-range order and central charge $\mathsf{c}=1$. Direct transitions between competing gapped phases can be continuous or weakly first order. We demonstrate that continuous phase transition lines have exotic critical properties. For example, a line of deconfined quantum critical points (between the Neel$^{\,}_{x}$ and Neel$^{\,}_{y}$ phases) described by Tomonaga-Luttinger liquid theory is terminated by the gFM$^{\,}_{z}$ phase at a Lifshitz tricritical point which exhibits spontaneous breaking of the continuous U(1) symmetry despite the locality and one-dimensionality of the Hamiltonian, contrary to a naive expectation from the Hohenberg-Mermin-Wagner-Coleman theorem. Furthermore, critical lines between symmetry-protected topological phases with different $\mathbb{Z}^{\,}_{2}$-symmetry breaking (e.g., Neel$^{\mathrm{SPT}}_{x}$ and Neel$^{\mathrm{SPT}}_{y}$) additionally retain low-energy boundary degrees of freedom, realizing symmetry-enriched criticality (or a gapless SPT phase). Our results reveal unconventional mechanisms by which competing symmetry breaking and topology generate ordered critical phases and multicriticality.

cond-mat.str-el↗

arXiv2026

Emanant and emergent symmetry-topological-order from low-energy spectrum

Low-energy emanant and emergent symmetries can be anomalous, higher-group, or non-invertible. A way to systematically capture the properties of such symmetries is through the topological orders in one-higher dimension, known as symmetry topological orders (symTOs). Consequently, identifying the emergent or emanant symmetry of a system is not simply a matter of determining its group structure, but rather of computing the corresponding symTO. In this work, we develop a method to compute the symTO of 1+1D systems by analyzing their low-energy spectra under closed boundary conditions with all possible symmetry twists. Following this approach, we show that the gapless antiferromagnetic (AF) spin-$1/2$ Heisenberg model possesses an exact emanant symTO corresponding to the $D_8$ quantum double, when the global symmetry is restricted to the $\mathbb{Z}_2^x \times \mathbb{Z}_2^z$ subgroup of the $SO(3)$ spin-rotation symmetry and lattice translations. Moreover, this model exhibits an emergent $SO(4)$ symmetry, whose exact components are described jointly by automorphisms of the $D_8$ quantum double and the $SO(3)$ spin-rotations. Using the condensable algebras of the emanant symTO, we further identify several other phases that may be accessible by modifying interactions among low-energy excitations: (1) a gapped dimer phase, connected to the AF phase via an $SO(4)$ rotation, (2) a commensurate collinear ferromagnetic phase that breaks translation by one site with a $ω\sim k^2$ mode, (3) an incommensurate, translation-symmetric ferromagnetic phase featuring both $ω\sim k^2$ and $ω\sim k$ modes, (4) and an incommensurate ferromagnetic phase that breaks translation by one site with both $ω\sim k^2$ and $ω\sim k$ modes.

cond-mat.str-el↗

arXiv2026

Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond

We extend the Symmetry Topological Field Theory (SymTFT) framework beyond internal symmetries by including geometric data that encode spacetime symmetries. Concretely, we enrich the SymTFT of an internal symmetry by spacetime symmetries and study the resulting symmetry-enriched topological (SET) order, which captures the interplay between the spacetime and internal symmetries. We illustrate the framework by focusing on symmetries in ${1+1}$D. To this end, we first analyze how gapped boundaries of ${2+1}$D SETs affect the enriching symmetry, and apply this within the SymTFT framework to gauging and detecting anomalies of the ${1+1}$D symmetry, as well as to classifying ${1+1}$D symmetry-enriched phases. We then consider quantum spin chains and explicitly construct the SymTFTs for three prototypical spacetime symmetries: lattice translations, spatial reflections, and time reversal. For lattice translations, the interplay with internal symmetries is encoded in the SymTFT by translations permuting anyons, which causes the continuum description of the SymTFT to be a foliated field theory. Using this, we elucidate the relation between Lieb-Schultz-Mattis (LSM) anomalies and modulated symmetries and classify modulated symmetry-protected topological (SPT) phases. For reflection and time-reversal symmetries, the interplay can additionally be encoded by symmetry fractionalization data in the SymTFT, and we identify mixed anomalies and study gauging for such examples.

cond-mat.str-el↗

arXiv2025

Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions

We present a scenario, in which a gapless extended phase serves as a "hub" connecting multiple symmetry-enriched deconfined quantum critical points. As a concrete example, we construct a lattice model with $\mathbb{Z}^{\,}_{2}\times \mathbb{Z}^{\,}_{2}\times \mathbb{Z}^{\,}_{2}$ symmetry for quantum spin-1/2 degrees of freedom that realizes four distinct gapful phases supporting antiferromagnetic long-range order and one extended incommensurate gapless ferromagnetic phase. The quantum phase transition between any two of the four gapped and antiferromagnetic phases goes through either a (deconfined) quantum critical point, a quantum tricritical point, or the incommensurate gapless ferromagnetic phase. In this phase diagram, it is possible to interpolate between four deconfined quantum critical points by passing through the extended gapless ferromagnetic phase. We identify the phases in the model and the nature of the transitions between them through a combination of analytical arguments and density matrix renormalization group studies.

cond-mat.str-el↗

arXiv2025

Phases with non-invertible symmetries in 1+1D $\unicode{x2013}$ symmetry protected topological orders as duality automorphisms

We explore 1+1 dimensional (1+1D) gapped phases in systems with non-invertible symmetries, focusing on symmetry-protected topological (SPT) phases (defined as gapped phases with non-degenerate ground states), as well as SPT orders (defined as the differences between gapped/gapless phases with identical bulk excitations spectrum). For group-like symmetries, distinct SPT phases share identical bulk excitations and always differ by SPT orders. However, for certain non-invertible symmetries, we discover novel SPT phases that have different bulk excitations and thus do not differ by SPT orders. Additionally, we also study the spontaneous symmetry-breaking (SSB) phases of non-invertible symmetries. Unlike group-like symmetries, non-invertible symmetries lack the concept of subgroups, which complicates the definition of SSB phases as well as their identification. This challenge can be addressed by employing the symmetry-topological-order (symTO) framework for the symmetry. The Lagrangian condensable algebras and automorphisms of the symTO facilitate the classification of gapped phases in systems with such symmetries, enabling the analysis of both SPT and SSB phases (including those that differ by SPT orders). Finally, we apply this methodology to investigate gapless phases in symmetric systems and to study gapless phases differing by SPT orders.

cond-mat.str-el↗

arXiv2025

(SPT-)LSM theorems from projective non-invertible symmetries

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations in a generalized $1+1$D quantum XY model based on group-valued qudits. This model is specified by a finite group $G$ and enjoys a projective $\mathsf{Rep}(G)\times Z(G)$ and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. However, this is not generally true for non-invertible symmetries, and we derive a condition on $G$ for the existence of an LSM anomaly. When this condition is not met, we prove an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak symmetry protected topological (SPT) state with non-trivial entanglement, for which we construct an example fixed-point Hamiltonian. The projectivity also affects the dual symmetries after gauging $\mathsf{Rep}(G)\times Z(G)$ sub-symmetries, giving rise to non-Abelian and non-invertible dipole symmetries, as well as non-invertible translations. We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. Throughout the paper, we develop techniques for gauging $\mathsf{Rep}(G)$ symmetry and inserting its symmetry defects on the lattice, which are applicable to other non-invertible symmetries.

cond-mat.str-el↗

arXiv2025

Deconfined classical criticality in the anisotropic quantum spin-$\frac{1}{2}$ XY model on the square lattice

The anisotropic quantum spin-1/2 XY model on a linear chain was solved by Lieb, Schultz, and Mattis in 1961 and shown to display a continuous quantum phase transition at the O(2) symmetric point separating two gapped phases with competing Ising long-range order. For the square lattice, the following is known. The two competing Ising ordered phases extend to finite temperatures, up to a boundary where a transition to the paramagnetic phase occurs, and meet at the O(2) symmetric critical line along the temperature axis that ends at a tricritical point at the Berezinskii-Kosterlitz-Thouless transition temperature where the two competing phases meet the paramagnetic phase. We show that the first-order zero-temperature (quantum) phase transition that separates the competing phases as a function of the anisotropy parameter is smoothed by thermal fluctuations into deconfined classical criticality.

cond-mat.str-el↗

arXiv2025

Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries

We investigate the gauging of higher-form finite Abelian symmetries and their sub-groups in quantum spin models in spatial dimensions $d=2$ and 3. Doing so, we naturally uncover gauged models with dual higher-group symmetries and potential mixed 't Hooft anomalies. We demonstrate that the mixed anomalies manifest as the symmetry fractionalization of higher-form symmetries participating in the mixed anomaly. Gauging is realized as an isomorphism or duality between the bond algebras that generate the space of quantum spin models with the dual generalized symmetry structures. We explore the mapping of gapped phases under such gauging related dualities for 0-form and 1-form symmetries in spatial dimension $d=2$ and 3. In $d=2$, these include several non-trivial dualities between short-range entangled gapped phases with 0-form symmetries and 0-form symmetry enriched Higgs and (twisted) deconfined phases of the gauged theory with possible symmetry fractionalizations. Such dualities also imply strong constraints on several unconventional, i.e., deconfined or topological transitions. In $d=3$, among others, we find, dualities between topological orders via gauging of 1-form symmetries. Hamiltonians self-dual under gauging of 1-form symmetries host emergent non-invertible symmetries, realizing higher-categorical generalizations of the Tambara-Yamagami fusion category.

cond-mat.str-el↗

arXiv2025

Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections

Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in ${1+1}$ dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models.

cond-mat.str-el↗

arXiv2024

Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries

Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) $S^{\,}_3$ symmetry and the other with non-invertible $\mathsf{Rep}(S^{\,}_3)$ symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1D symmetry-topological-order (SymTO) of type $\mathrm{JK}^{\,}_4\boxtimes \overline{\mathrm{JK}}^{\,}_4$. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual $S^{\,}_3$-symmetric and $\mathsf{Rep}(S^{\,}_3)$-symmetric models.

cond-mat.str-el↗

arXiv2024

Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground state only contains short-range entanglement and does not break symmetries spontaneously, they generically realize crystalline fermionic symmetry-protected topological phases (cFSPTs), supporting gapless modes at the boundaries or at the lattice defects. Here, we provide an exhaustive classification of cFSPTs in two dimensions with $\mathrm{U}(1)$ charge-conservation and spinful time-reversal symmetries, namely, those generically present in spin-orbit coupled insulators, for any of the 17 wallpaper groups. It has been shown that the classification of cFSPTs can be understood from appropriate real-space decorations of lower-dimensional subspaces, and we expose how these relate to the Wyckoff positions of the lattice. We find that all nontrivial one-dimensional decorations require electronic interactions. Furthermore, we provide model Hamiltonians for various decorations, and discuss the signatures of cFSPTs. This classification paves the way to further explore topological interacting insulators, providing the backbone information in generic model systems and ultimately in experiments.

cond-mat.str-el↗

arXiv2024

Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains

Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the zero-temperature phase diagrams of quantum lattice Hamiltonians (always assumed to be local in this paper). LSM theorems have recently been interpreted as the lattice counterparts to mixed 't Hooft anomalies in quantum field theories that arise from a combination of crystalline and global internal symmetry groups. Accordingly, LSM theorems have been reinterpreted as LSM anomalies. In this work, we provide a systematic diagnostic for LSM anomalies in one spatial dimension. We show that gauging subgroups of the global internal symmetry group of a quantum lattice model obeying an LSM anomaly delivers a dual quantum lattice Hamiltonian such that its internal and crystalline symmetries mix non-trivially through a group extension. This mixing of crystalline and internal symmetries after gauging is a direct consequence of the LSM anomaly, i.e., it can be used as a diagnostic of an LSM anomaly. We exemplify this procedure for a quantum spin-1/2 chain obeying an LSM anomaly resulting from combining a global internal $\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{\,}_{2}$ symmetry with translation or reflection symmetry. We establish a triality of models by gauging a $\mathbb{Z}^{\,}_{2}\subset\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{\,}_{2}$ symmetry in two ways, one of which amounts to performing a Kramers-Wannier duality, while the other implements a Jordan-Wigner duality. We discuss the mapping of the phase diagram of the quantum spin-1/2 $XYZ$ chains under such a triality. We show that the deconfined quantum critical transitions between Neel and dimer orders are mapped to either topological or conventional Landau-Ginzburg transitions. Finally, we extend our results to $\mathbb{Z}^{\,}_{n}$ clock models and provide a reinterpretation of the dual internal symmetries in terms of $\mathbb{Z}^{\,}_{n}$ charge and dipole symmetries.

cond-mat.str-el↗

arXiv2023

Single monkey-saddle singularity of a Fermi surface and its instabilities

Fermi surfaces can undergo sharp transitions under smooth changes of parameters. Such transitions can have a topological character, as is the case when a higher-order singularity, one that requires cubic or higher-order terms to describe the electronic dispersion near the singularity, develops at the transition. When time-reversal and inversion symmetries are present, odd singularities can only appear in pairs within the Brillouin zone. In this case, the combination of the enhanced density of states that accompany these singularities and the nesting between the pairs of singularities leads to interaction driven instabilities. We present examples of single $n=3$ (monkey saddle) singularities when time-reversal and inversion symmetries are broken. We then turn to the question of what instabilities are possible when the singularities are isolated. For spinful electrons, we find that the inclusion of repulsive interactions destroys any isolated monkey-saddle singularity present in the noninteracting spectrum by developing Stoner or Lifshitz instabilities. In contrast, for spinless electrons and at the mean-field level, we show that an isolated monkey-saddle singularity can be stabilized in the presence of short-range repulsive interactions.

cond-mat.str-el↗

arXiv2022

Elementary derivation of the stacking rules of invertible fermionic topological phases in one dimension

Invertible fermionic topological (IFT) phases are gapped phases of matter with nondegenerate ground states on any closed spatial manifold. When open boundary conditions are imposed, nontrivial IFT phases support gapless boundary degrees of freedom. Distinct IFT phases in one-dimensional space with an internal symmetry group $G^{\,}_{f}$ have been characterized by a triplet of indices $([(ν,ρ)],[μ])$. Our main result is an elementary derivation of the fermionic stacking rules of one-dimensional IFT phases for any given internal symmetry group $G^{\,}_{f}$ from the perspective of the boundary, i.e., we give an explicit operational definition for the boundary representation $([(ν^{\,}_{\wedge},ρ^{\,}_{\wedge})],[μ^{\,}_{\wedge}])$ obtained from stacking two IFT phases characterized by the triplets of boundary indices $([(ν^{\,}_{1},ρ^{\,}_{1})],[μ^{\,}_{1}])$ and $([(ν^{\,}_{2},ρ^{\,}_{2})],[μ^{\,}_{2}])$, respectively.

cond-mat.str-el↗

arXiv2021

Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries

We prove two Lieb-Schultz-Mattis type theorems that apply to any translationally invariant and local fermionic $d$-dimensional lattice Hamiltonian for which fermion-number conservation is broken down to the conservation of fermion parity. We show that when the internal symmetry group $G^{\,}_{f}$ is realized locally (in a repeat unit cell of the lattice) by a nontrivial projective representation, then the ground state cannot be simultaneously nondegenerate, symmetric (with respect to lattice translations and $G^{\,}_{f}$), and gapped. We also show that when the repeat unit cell hosts an odd number of Majorana degrees of freedom and the cardinality of the lattice is even, then the ground state cannot be simultaneously nondegenerate, gapped, and translation symmetric.

cond-mat.str-el↗

arXiv2021

Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries

We study the stability of topological crystalline superconductors in the symmetry class DIIIR and in two-dimensional space when perturbed by quartic contact interactions. It is known that no less than eight copies of helical pairs of Majorana edge modes can be gapped out by an appropriate interaction without spontaneously breaking any one of the protecting symmetries. Hence, the noninteracting classification $\mathbb{Z}$ reduces to $\mathbb{Z}^{\,}_{8}$ when these interactions are present. It is also known that the stability when there are less than eight modes can be understood in terms of the presence of topological obstructions in the low-energy bosonic effective theories, which prevent opening of a gap. Here, we investigate the stability of the edge theories with four, two, and one edge modes, respectively. We give an analytical derivation of the topological term for the first case, because of which the edge theory remains gapless. For two edge modes, we employ bosonization methods to derive an effective bosonic action. When gapped, this bosonic theory is necessarily associated to the spontaneous symmetry breaking of either one of time-reversal or reflection symmetry whenever translation symmetry remains on the boundary. For one edge mode, stability is explicitly established in the Majorana representation of the edge theory.

cond-mat.str-el↗

arXiv2020

Majorana zero modes in a quantum wire platform without Rashba spin-orbit coupling

We propose a platform for engineering helical fermions in a hybridized double-quantum-wire setup. When our setup is proximity coupled to an $s$-wave superconductor it can become a class $D$ topological superconductor exhibiting Majorana zero modes. The goal of this proposal is to expand the group of available Hamiltonians to those without strong Rashba spin-orbit interactions which are essential to many other approaches. Furthermore, we show that there exist electron-electron interactions that stabilize fractional excitations which obey $\mathbb{Z}^{\,}_{3}$ parafermionic algebra.

cond-mat.str-el↗

arXiv2020

Magnetic structure and spin waves in the frustrated ferro-antiferromagnet Pb$_2$VO(PO$_4$)$_2$

Single crystal neutron diffraction, inelastic neutron scattering and electron spin resonance experiments are used to study the magnetic structure and spin waves in Pb$_2$VO(PO$_4$)$_2$, a prototypical layered $S=1/2$ ferromagnet with frustrating next nearest neighbor antiferromagnetic interactions. The observed excitation spectrum is found to be inconsistent with a simple square lattice model previously proposed for this material. At least four distinct exchange coupling constants are required to reproduce the measured spin wave dispersion. The degree of magnetic frustration is correspondingly revised and found to be substantially smaller than in all previous estimates.

cond-mat.str-el↗