arXiv subjects

Dominic V. Else

Publications and source records attributed to Dominic V. Else.

At least 19 recordsLinked to original sources

arXiv2026

A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems

In mixed states of quantum systems, symmetries come in two types: strong and weak. Furthermore, it has been argued that in quantum many-body systems, strong symmetries can be "spontaneously broken" down to weak symmetries. An issue is that as previously formulated, such "strong-to-weak symmetry breaking" appears to be a fairly non-local effect. In this paper, we show how to understand and diagnose strong symmetries and strong-to-weak symmetry breaking in an explicitly local way. Our main technical tool is a rigorous definition of strong symmetry in the limit of infinite volume, which generalizes the conventional finite-volume definitions, and for which we give several equivalent formulations, including one involving the concept of "local charge coherence". Finally, we introduce von Neumann systems, which in infinite-volume symmetries are intermediate between strong and weak symmetries. We derive a Lieb-Schultz-Mattis type anomaly constraint for von Neumann symmetries (and therefore, in particular, strong symmetries) in quantum spin chains.

quant-ph↗

arXiv2026

In search of diabolical critical points

A phase transition is an example of a ``topological defect'' in the space of parameters of a quantum or classical many-body systems. In this paper, we consider phase diagram topological defects of higher codimension. These have the property that equilibrium states undergo some kind of non-trivial winding as one moves around the defect. We show that such topological defects exist even in classical statistical mechanical systems, and describe their general structure in this context. We then introduce the term ``diabolical critical point'' (DCP), which is a higher-codimension analog of a continuous phase transition, with the proximate phases of matter replaced by the non-trivial winding of the proximate equilibrium states. We propose conditions under which a system can have a stable DCP. We also discuss some examples of stable DCPs in (1+1)-dimensional quantum systems.

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arXiv2025

Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order

Many-body localization (MBL) lends remarkable robustness to nonequilibrium phases of matter. Such phases can show topological and symmetry breaking order in their ground and excited states, but they may also belong to an anomalous localized topological phase (ALT phase). All eigenstates in an ALT phase are trivial, in that they can be deformed to product states, but the entire Hamiltonian cannot be deformed to a trivial localized model without going through a delocalization transition. Using a correspondence between MBL phases with short-ranged entanglement and locality preserving unitaries - called quantum cellular automata (QCA) - we reduce the classification of ALT phases to that of QCA. This method extends to periodically (Floquet) and quasiperiodically driven ALT phases, and captures anomalous Floquet phases within the same framework as static phases. We considerably develop the study of the topology of QCA, allowing us to classify static and driven ALT phases in low dimensions. The QCA framework further generalizes to include symmetry-enriched ALT phases (SALT phases) - which we also classify in low dimensions - and provides a large class of soluble models suitable for realization in quantum simulators. In systematizing the study of ALT phases, we both greatly extend the classification of interacting nonequilibrium systems and clarify a confusion in the literature which implicitly equates nontrivial Hamiltonians with nontrivial ground states.

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arXiv2025

Anomalies of global symmetries on the lattice

't Hooft anomalies of global symmetries play a fundamental role in quantum many-body systems and quantum field theory (QFT). In this paper, we make a systematic analysis of lattice anomalies - the analog of 't Hooft anomalies in lattice systems - for which we give a precise definition. Crucially, a lattice anomaly is not a feature of a specific Hamiltonian, but rather is a topological invariant of the symmetry action. The controlled setting of lattice systems allows for a systematic and rigorous treatment of lattice anomalies, shorn of the technical challenges of QFT. We find that lattice anomalies reproduce the expected properties of QFT anomalies in many ways, but also have crucial differences. In particular, lattice anomalies and QFT anomalies are not, contrary to a common expectation, in one-to-one correspondence, and there can be non-trivial anomalies on the lattice that are infrared (IR) trivial: they admit symmetric trivial gapped ground states, and map to trivial QFT anomalies at low energies. Nevertheless, we show that lattice anomalies (including IR-trivial ones) have a number of interesting consequences in their own right, including connections to commuting projector models, phases of many-body localized (MBL) systems, and quantum cellular automata (QCA). We make substantial progress on the classification of lattice anomalies and develop several theoretical tools to characterize their consequences on symmetric Hamiltonians. Our work places symmetries of quantum many-body lattice systems into a unified theoretical framework and may also suggest new perspectives on symmetries in QFT.

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arXiv2025

't Hooft anomalies in metals

I review some recent results on understanding the physics of metals in an exact non-perturbative way through the powerful field-theoretic concepts of emergent symmetries and 't Hooft anomalies. A 't Hooft anomaly is a discrete topological property that quantum field theories with global symmetries can have. I explain how many of the properties of metals can in fact be viewed as direct consequences of the anomaly. This allows a structural understanding of metals, including non-Fermi liquids, to be obtained even in the absence of any exact solution for the strongly coupled dynamics. I then outline the main limitations and outstanding questions.

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arXiv2024

Anomalous continuous symmetries and quantum topology of Goldstone modes

We consider systems in which a continuous symmetry $G$, which may be anomalous, is spontaneously broken to an anomaly-free subgroup $H$ such that the effective action for the Goldstone modes contains topologically non-trivial terms. If the original system has trivial $G$ anomaly, it is known that the possible topological terms are fully determined by SPT or SET invariants of the residual $H$ symmetry. Here we address the more general setting in which the $G$ symmetry has an anomaly. We argue that in general, the appropriate concept to consider is the "compatibility relation" between the Goldstone invariants and the $G$ anomaly. In the case where the Goldstone modes can be gapped out to obtain invertible families (i.e. without any topological order), we give an explicit mathematical scheme to construct the desired compatibility relation. We also address the case where gapping out the Goldstone modes leads to a family of topologically ordered states. We discuss several examples including the canonical Thouless pump, the quantum Hall ferromagnet, pumps arising from breaking $\text{U}(1)$ symmetry at the boundary of topological insulators in two and three dimensions, and pumps classified by the higher Chern number.

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arXiv2023

Holographic models of non-Fermi liquid metals revisited: an effective field theory approach

Accessing the physics of strongly coupled metals in a controlled way is a challenging problem in theoretical condensed matter physics. In this paper, we revisit the possibility of understanding strongly coupled metals through a holographic duality with a weakly coupled gravitational theory in one higher dimension (i.e.\ a suitable generalization of the "AdS/CFT duality". Previous attempts at devising holographic models of strongly coupled metals have suffered from severe drawbacks; for example, they do not even seem to be able to describe a Fermi surface that satisfies Luttinger's theorem, which is ought to be a core requirement in any physically reasonable model of a metal. Here, we propose a radically different approach to constructing holographic models of strongly coupled metals. The idea is that for applications, it should be sufficient to construct a holographic dual of the effective field theory that controls the infra-red physics of the metal. We invoke recent work that has identified a precise criterion for such an effective field theory to be "emergeable" from a continuum ultra-violet (UV) theory at nonzero charge density (or its equivalent in lattice models, namely an incommensurate charge filling). We show that imposing this criterion leads to a holographic model of a strongly coupled metal with physically reasonable properties, including a Fermi surface satisfying Luttinger's theorem. We discuss a possible physical interpretation of our results.

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arXiv2023

Collisionless dynamics of general non-Fermi liquids from hydrodynamics of emergent conserved quantities

Given the considerable theoretical challenges in understanding strongly coupled metals and non-Fermi liquids, it is valuable to have a framework to understand properties of metals that are universal, in the sense that they must hold in any metal. It has previously been argued that an infinite-dimensional emergent symmetry group is such a property, at least for clean, compressible metals. In this paper, we will show that such an emergent symmetry group has very strong implications for the dynamics of the metal. Specifically, we show that consideration of the hydrodynamics of the associated infinitely many emergent conserved quantities automatically recovers the collisionless Boltzmann equation that governs the dynamics of a Fermi liquid. Therefore, the hydrodynamic prediction is that in the low-temperature, collisionless regime where the emergent conservation laws hold, the dynamics and response to external fields of a general spinless metal will be identical to a Fermi liquid. We discuss some potential limitations to this general statement, including the possibility of non-hydrodynamic modes. We also report some interesting differences in the case of spinful metals.

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arXiv2023

Loop current fluctuations and quantum critical transport

We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the "Hertz-Millis" type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving $N$ species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, $σ(ω>0)\simω^{-2/z}$, where $z$ is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large $N$ expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical $N = 1$ system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, $σ(ω>0) \sim ω^{-2(z-2)/z}$, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.

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arXiv2022

Gifts from anomalies: Exact results for Landau phase transitions in metals

Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in "Hertz-Millis" theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, $\mathbf{q}=0$, is a constant independent of frequency, and the real part of the optical conductivity, $σ(ω)$, is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.

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arXiv2022

Critical drag as a mechanism for resistivity

A quantum many-body system with a conserved electric charge can have a DC resistivity that is either exactly zero (implying it supports dissipationless current) or nonzero. Exactly zero resistivity is related to conservation laws that prevent the current from degrading. In this paper, we carefully examine the situations in which such a circumstance can occur. We find that exactly zero resistivity requires either continuous translation symmetry, or an internal symmetry that has a certain kind of "mixed anomaly" with the electric charge. (The symmetry could be a generalized global symmetry associated with the emergence of unbreakable loop or higher dimensional excitations.) However, even if one of these is satisfied, we show that there is still a mechanism to get nonzero resistivity, through critical fluctuations that drive the susceptibility of the conserved quantity to infinity; we call this mechanism "critical drag". Critical drag is thus a mechanism for resistivity that, unlike conventional mechanisms, is unrelated to broken symmetries. We furthermore argue that an emergent symmetry that has the appropriate mixed anomaly with electric charge is in fact an inevitable consequence of compressibility in systems with lattice translation symmetry. Critical drag therefore seems to be the only way (other than through irrelevant perturbations breaking the emergent symmetry, that disappear at the renormalization group fixed point) to get nonzero resistivity in such systems. Finally, we present a very simple and concrete model -- the "Quantum Lifshitz Model" -- that illustrates the critical drag mechanism as well as the other considerations of the paper.

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arXiv2021

Topological Goldstone phases of matter

We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a \emph{topologically non-trivial} way, which, roughly, means that the action for the Goldstone modes contains a quantized topological term, and could manifest in, for example, non-trivial quantum numbers of topological defects of the order parameter. We show that, in fact, such a scenario can occur only when the system is in a non-trivial symmetry-protected topological (SPT) or symmetry-enriched topological (SET) phase with respect to the residual symmetry; or alternatively, if the original symmetry before spontaneous symmetry breaking acts on the system in an "anomalous" way. Our arguments are based on a general correspondence between topological defects of the order parameter and topological defects of a background gauge field for the residual symmetry.

cond-mat.str-el↗

arXiv2021

Strange metals as ersatz Fermi liquids

A long standing mystery of fundamental importance in correlated electron physics is to understand strange non-Fermi liquid metals that are seen in diverse quantum materials. A striking experimental feature of these metals is a resistivity that is linear in temperature ($T$). In this paper we ask what it takes to obtain such non-Fermi liquid physics down to zero temperature in a translation invariant metal. If in addition the full frequency ($ω$) dependent conductivity satisfies $ω/T$ scaling, we argue that the $T$-linear resistivity must come from the intrinsic physics of the low energy fixed point. Combining with earlier arguments that compressible translation invariant metals are `ersatz Fermi liquids' with an infinite number of emergent conserved quantities, we obtain powerful and practical conclusions. We show that there is necessarily a diverging susceptibility for an operator that is odd under inversion/time reversal symmetries, and has zero crystal momentum. We discuss a few other experimental consequences of our arguments, as well as potential loopholes which necessarily imply other exotic phenomena.

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arXiv2021

Quantum many-body topology of quasicrystals

In this paper, we characterize quasicrystalline interacting topological phases of matter i.e., phases protected by some quasicrystalline structure. We show that the elasticity theory of quasicrystals, which accounts for both "phonon" and "phason" modes, admits non-trivial quantized topological terms with far richer structure than their crystalline counterparts. We show that these terms correspond to distinct phases of matter and also uncover intrinsically quasicrystalline phases, which have no crystalline analogues. For quasicrystals with internal $\mathrm{U}(1)$ symmetry, we discuss a number of interpretations and physical implications of the topological terms, including constraints on the mobility of dislocations in $d=2$ quasicrystals and a quasicrystalline generalization of the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem. We then extend these ideas much further and address the complete classification of quasicrystalline topological phases, including systems with point-group symmetry as well as non-invertible phases. We hence obtain the "Quasicrystalline Equivalence Principle," which generalizes the classification of crystalline topological phases to the quasicrystalline setting.

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arXiv2021

Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals

A system with charge conservation and lattice translation symmetry has a well-defined filling $ν$, which is a real number representing the average charge per unit cell. We show that if $ν$ is fractional (i.e. not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems. The most powerful constraint comes about if $ν$ is continuously tunable (i.e. the system is charge-compressible), in which case we show that the low-energy theory must have a very large emergent symmetry group -- larger than any compact Lie group. An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved. We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics. We call a system with this property an "ersatz Fermi liquid". We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttinger's theorem (which is thus extended to a large class of non-Fermi liquids) and periodic "quantum oscillations" in the response to an applied magnetic field. We also establish versions of Luttinger's theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators. Our work makes connection between filling constraints and the theory of symmetry-protected topological (SPT) phases, in particular through the concept of " 't Hooft anomalies".

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arXiv2021

Observation of a prethermal discrete time crystal

The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven phase without disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating is suppressed not by disorder-induced many-body localization, but instead via high-frequency driving, leading to an expansive time window where non-equilibrium phases can emerge. We observe a number of key features that distinguish the PDTC from its many-body-localized disordered counterpart, such as the drive-frequency control of its lifetime and the dependence of time-crystalline order on the energy density of the initial state. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing and studying intrinsically out-of-equilibrium phases of matter.

quant-ph↗

arXiv2020

Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems

The Lieb-Schultz-Mattis (LSM) theorem states that a spin system with translation and spin rotation symmetry and half-integer spin per unit cell does not admit a gapped symmetric ground state lacking fractionalized excitations. That is, the ground state must be gapless, spontaneously break a symmetry, or be a gapped spin liquid. Thus, such systems are natural spin-liquid candidates if no ordering is found. In this work, we give a much more general criterion that determines when an LSM-type theorem holds in a spin system. For example, we consider quantum magnets with arbitrary space group symmetry and/or spin-orbit coupling. Our criterion is intimately connected to recent work on the general classification of topological phases with spatial symmetries and also allows for the computation of an "anomaly" associated with the existence of an LSM theorem. Moreover, our framework is also general enough to encompass recent works on "SPT-LSM" theorems where the system admits a gapped symmetric ground state without fractionalized excitations, but such a ground state must still be non-trivial in the sense of symmetry-protected topological (SPT) phases.

cond-mat.str-el↗

arXiv2020

Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasi-crystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry protected topological phases.

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