| 1. |
- Aksoy, Omer M., et al.
(författare)
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Single monkey-saddle singularity of a Fermi surface and its instabilities
- 2023
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 107:20
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Tidskriftsartikel (refereegranskat)abstract
- 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 accompanies these singularities and the nesting between the pairs of singularities leads to interaction-driven instabilities. We present examples of single n = 3 (monkeysaddle) 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.
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| 2. |
- Bhardwaj, Lakshya, et al.
(författare)
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Non-invertible higher-categorical symmetries
- 2023
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 14:1
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Tidskriftsartikel (refereegranskat)abstract
- We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also discuss fusions of topological defects, which involve condensations/gaugings of higher-categorical symmetries localized on the worldvolumes of topological defects. Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion. This is not possible in the standard description of higher-categories. We explain that the dimension-changing fusions are understood as higher-morphisms of the higher-category describing the symmetry. We also discuss how a 0-form sub-symmetry of a higher-categorical symmetry can be gauged and describe the higher-categorical symmetry of the theory obtained after gauging. This provides a procedure for constructing non-invertible higher-categorical symmetries starting from invertible higher-form or higher-group symmetries and gauging a 0-form symmetry. We illustrate this procedure by constructing non-invertible 2-categorical symmetries in 4d gauge theories and non-invertible 3-categorical symmetries in 5d and 6d theories. We check some of the results obtained using our approach against the results obtained using a recently proposed approach based on’t Hooft anomalies.
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| 3. |
- Bhardwaj, Lakshya, et al.
(författare)
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Non-invertible symmetry webs
- 2023
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 15:4
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Tidskriftsartikel (refereegranskat)abstract
- Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with G 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [1]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups G, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions.
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| 4. |
- Bhardwaj, Lakshya, et al.
(författare)
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Unifying constructions of non-invertible symmetries
- 2023
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Ingår i: SciPost Physics. - : SciPost Foundation. - 2542-4653. ; 15:3
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Tidskriftsartikel (refereegranskat)abstract
- In the past year several constructions of non-invertible symmetries in Quantum Field Theory in d ≥ 3 have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta defects, which generalize the notion of theta-angles, and allow the construction of universal and non-universal topological symmetry defects. We complement this physical analysis by proposing a mathematical framework (based on higher-fusion categories) that converts the physical construction of non-invertible symmetries into a concrete computational scheme.
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| 5. |
- Choo, Kenny, et al.
(författare)
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Thermal and dissipative effects on the heating transition in a driven critical system
- 2022
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 13:5
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Tidskriftsartikel (refereegranskat)abstract
- We study the dissipative dynamics of a periodically driven inhomogeneous critical lattice model in one dimension. The closed system dynamics starting from pure initial states is well-described by a driven Conformal Field Theory (CFT), which predicts the existence of both heating and non-heating phases in such systems. Heating is inhomogeneous and is manifested via the emergence of black-hole like horizons in the system. The robustness of this CFT phenomenology when considering thermal initial states and open systems remains elusive. First, we present analytical results for the Floquet CFT time evolution for thermal initial states. Moreover, using exact calculations of the time evolution of the lattice density matrix, we demonstrate that for short and intermediate times, the closed system phase diagram comprising heating and non-heating phases, persists for thermal initial states on the lattice. Secondly, in the fully open system with boundary dissipators, we show that the nontrivial spatial structure of the heating phase survives particle-conserving and non-conserving dissipations through clear signatures in mutual information and energy density evolution.
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| 6. |
- Datta, Shouvik, et al.
(författare)
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Marginal quenches and drives in Tomonaga-Luttinger liquids
- 2023
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 14:5
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Tidskriftsartikel (refereegranskat)abstract
- We study Tomonaga-Luttinger liquids thrown out of equilibrium by marginal deformations in the form of interaction modulations. This is modeled by quenching or periodically driving the Luttinger parameter or, equivalently, the compactification radius of the free boson conformal field theory between two different values. We obtain exact analytical results for the evolution of the Loschmidt echo and observables such as the particle and energy densities. Starting from generic initial states, the quench dynamics are shown to exhibit revivals and temporal orthogonalities. For the periodic drive, we show stability or instability of time-evolved physical quantities dependent on the drive parameters. We also compare the corresponding marginally deformed thermal density matrices by non-perturbatively evaluating their Rényi divergence as a Euclidean quench. All the dynamics are shown to be crucially dependent on the ratio of the Luttinger parameters, which corresponds to the Zamolodchikov distance in the space of marginal deformations. Our setup is equivalently interpreted as the dynamics of the bosonic string upon instantaneous changes of the target-space radius.
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| 7. |
- Delcamp, Clement, et al.
(författare)
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Higher categorical symmetries and gauging in two-dimensional spin systems
- 2024
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Ingår i: SciPost Physics. - : SciPost Foundation. - 2542-4653. ; 16:4
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Tidskriftsartikel (refereegranskat)abstract
- We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. Our framework relies on an approach to dualities whereby dual quantum lattice models only differ in a choice of module 2-category over some input fusion 2-category. Given an arbitrary two-dimensional spin system with an ordinary symmetry, we explain how to perform the (twisted) gauging of any of its sub-symmetries. We then demonstrate that the resulting model has a symmetry structure encoded into the Morita dual of the input fusion 2-category with respect to the corresponding module 2-category. We exemplify this approach by specialising to certain finite group generalisations of the transversefield Ising model, for which we explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.
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| 8. |
- Fleckenstein, Christoph, et al.
(författare)
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Non-Hermitian topology in monitored quantum circuits
- 2022
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 4:3
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Tidskriftsartikel (refereegranskat)abstract
- We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model. We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked. The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits. For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system. Importantly, our monitored circuit realization allows direct access to steady-state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model. We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases.
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| 9. |
- Li, Ming-Hao, et al.
(författare)
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Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
- 2022
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 106:12
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Tidskriftsartikel (refereegranskat)abstract
- We show that the gapless boundary signatures-namely, chiral/helical hinge modes or localized zero modes- of three-dimensional higher-order topological insulators and superconductors with inversion symmetry can be gapped without symmetry breaking upon the introduction of non-Abelian surface topological order. In each case, the fractionalization pattern that appears on the surface is "anomalous" in the sense that it can be made consistent with symmetry only on the surface of a three-dimensional higher-order insulator/superconductor. Our results show that the interacting manifestation of higher-order topology is the appearance of "anomalous gapped boundaries" between distinct topological orders whose quasiparticles are related by inversion, possibly in conjunction with other protecting symmetries such as time-reversal symmetry and charge conservation.
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| 10. |
- Moradi, Heidar, et al.
(författare)
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Topological holography : Towards a unification of Landau and beyond-Landau physics
- 2023
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Ingår i: SciPost Physics Core. - : Stichting SciPost. - 2666-9366. ; 6:4
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Tidskriftsartikel (refereegranskat)abstract
- We outline a holographic1 framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with a global symmetry in one lower dimension. The global symmetry naturally serves as an input for the topological order. In particular, we holographically construct a String Operator Algebra (SOA) which is the building block of symmetric quantum systems with a given symmetry G in one lower dimension. This exposes a vast web of dualities which act on the space of Gsymmetric quantum systems. The SOA facilitates the classification of gapped phases as well as their corresponding order parameters and fundamental excitations, while dualities help to navigate and predict various corners of phase diagrams and analytically compute universality classes of phase transitions. A novelty of the approach is that it treats conventional Landau and unconventional topological phase transitions on an equal footing, thereby providing a holographic unification of these seemingly-disparate domains of understanding. We uncover a new feature of gapped phases and their multi-critical points, which we dub fusion structure, that encodes information about which phases and transitions can be dual to each other. Furthermore, we discover that self-dual systems typically posses emergent non-invertible, i.e., beyond group-like symmetries. We apply these ideas to 1 + 1d quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in 2 + 1d. We predict the phase diagrams of various concrete spin models, and analytically compute the full conformal spectra of non-trivial quantum phase transitions, which we then verify numerically.
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