arXiv subjects

Alexander Hickey

Publications and source records attributed to Alexander Hickey.

6 recordsLinked to original sources

arXiv2026

Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices

Infrared singularities of gapless Goldstone modes preclude magnetic long-range order at finite temperature in conventional two-dimensional systems. By studying the spin-$S$ Heisenberg model on regular tilings of the hyperbolic plane, we show that this obstruction is absent in negatively curved space. Using spin-wave theory, we find that the zero-energy collective modes required by symmetry carry vanishing local spectral weight and are separated from the thermodynamic bulk magnon continuum by a finite gap in the bulk local spectral density. As a result, local transverse correlations remain short ranged, with a finite correlation length, despite the presence of Goldstone modes associated with the broken SO(3) spin-rotation symmetry. Stronger negative curvature is found to suppress quantum fluctuations in bulk thermodynamic quantities, pushing the ordered state toward "mean-field-like" behavior. We further estimate the ordering temperature from the thermal spin-wave correction to the ordered moment. These results establish hyperbolic geometry as a route to finite-temperature magnetic order that circumvents the Mermin-Wagner obstruction without breaking or modifying the continuous symmetry.

cond-mat.str-el↗

arXiv2025

Universal temperature-dependent power law excitation gaps in frustrated quantum spin systems harboring order-by-disorder

When magnetic moments are subject to competing or frustrated interactions, continuous degeneracies that are not protected by any symmetry of the parent Hamiltonian can emerge at the classical (mean-field) level. Such "accidental" degeneracies are often lifted by both thermal and quantum fluctuations via a mechanism known as order-by-disorder (ObD). The leading proposal to detect and characterize ObD in real materials, in a way that quantitatively distinguishes it from standard energetic selection, is to measure a small fluctuation-induced pseudo-Goldstone gap in the excitation spectrum. While the properties of this gap are known to leading order in the spin wave interactions, in both the zero-temperature and classical limits, the pseudo-Goldstone (PG) gap in quantum magnets at finite temperature has yet to be characterized. Using non-linear spin wave theory, we compute the PG gap to leading order in a $1/S$ expansion at low temperature for a variety of frustrated quantum spin systems. We also develop a formalism to calculate the PG gap in a way that solely uses linear spin-wave theory, circumventing the need to carry out tedious quantum many-body calculations. We argue that, at leading order, the PG gap acquires a distinct power-law temperature dependence, proportional to either $T^{d+1}$ or $T^{d/2+1}$ depending on the gapless dispersion of the PG mode predicted at the mean-field level. Finally, we examine the implications of these results for the pyrochlore oxide compound Er$_2$Ti$_2$O$_7$, for which there is compelling evidence of ObD giving rise to the experimentally observed long-range order.

cond-mat.str-el↗

arXiv2024

Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions

Order-by-disorder, whereby fluctuations lift an accidental classical ground state degeneracy to stabilize a subset of ordered states, is a recurrent and prominent theme in the field of frustrated magnetism where magnetic moments are subject to competing interactions. Thus far, such a phenomenon has been discussed in systems where the quantum ground state is not a classical product state. In such a case, both thermal and quantum fluctuations act to lift the accidental classical degeneracy, begging the question of whether one mechanism of order-by-disorder is possible without the other. In this paper, we present results exposing an uncharted route to order-by-disorder, one without quantum zero-point fluctuations, in the ferromagnetic pyrochlore Heisenberg system with the Dzyaloshinskii-Moriya (DM) interaction as the leading perturbation. We prove that any colinear ferromagnetic state is an exact eigenstate while thermal fluctuations give rise to a preference in the magnetization direction. Using linear spin wave theory, we find that the anisotropy appears at lowest order as a sub-leading term in the low-temperature expansion of the free energy, proportional to $T^{7/2}$. Our results thus show that the phenomenon of thermal order-by-disorder can occur even in the absence of quantum zero-point fluctuations driving quantum order-by-disorder, this being so in particular when the accidentally degenerate ground state of the classical model turns out to be an exact eigenstate of the quantum version of the model. In addition, we find that when the DM interaction is large, the fully polarized ferromagnetic ground state becomes unstable for a spin-$\frac{1}{2}$ system within the framework of non-linear spin wave theory, a result that is presumably closely related to the recent report of a quantum spin liquid in this spin-$\frac{1}{2}$ model reported in [https://doi.org/10.1073/pnas.2403487121].

cond-mat.str-el↗

arXiv2023

Current-Induced Spin Accumulation and Magnetoresistance in Chiral Semimetals

Weyl fermions possess the property of spin-momentum locking: the expectation value of the spin is parallel or antiparallel to the momentum at any given point in the Brillouin zone in the vicinity of a Weyl node. This is a direct consequence of the fact that Weyl nodes are monopoles of the Berry curvature, and in this sense an expression of the nontrivial Weyl electronic structure topology. Thanks to this property, an isolated Weyl node produces a large spin accumulation in response to a charge current, $\hbar/2$ per electron, similar to surface states of time-reversal invariant topological insulators. However, in bulk Weyl semimetals, the nodes must occur in pairs of opposite chirality and, when the nodes are at the same energy, the effect cancels out. Here we show that this cancellation is avoided in chiral semimetals, in which Weyl nodes of opposite chirality occur at different energies due to broken mirror symmetry. We find that the spin accumulation is maximized when the Fermi energy coincides with one of the nodes in a pair and reaches the same value as for an isolated node in this case. Moreover, we demonstrate the existence of a distinct magnetoresistance mechanism, closely related to this current-induced spin accumulation.

cond-mat.mes-hall↗

arXiv2021

Emergent anomalies and generalized Luttinger theorems in metals and semimetals

Luttinger's theorem connects a basic microscopic property of a given metallic crystalline material, the number of electrons per unit cell, to the volume, enclosed by its Fermi surface, which defines its low-energy observable properties. Such statements are valuable since, in general, deducing a low-energy description from microscopics, which may perhaps be regarded as the main problem of condensed matter theory, is far from easy. In this paper we present a unified framework, which allows one to discuss Luttinger theorems for ordinary metals, as well as closely analogous exact statements for topological (semi)metals, whose low-energy description contains either discrete point or continuous line nodes. This framework is based on the 't Hooft anomaly of the emergent charge conservation symmetry at each point on the Fermi surface, a concept recently proposed by Else, Thorngren and Senthil [Phys. Rev. X 11, 021005 (2021)]. We find that the Fermi surface codimension $p$ plays a crucial role for the emergent anomaly. For odd $p$, such as ordinary metals ($p=1$) and magnetic Weyl semimetals ($p=3$), the emergent symmetry has a generalized chiral anomaly. For even $p$, such as graphene and nodal line semimetals (both with $p=2$), the emergent symmetry has a generalized parity anomaly. When restricted to microscopic symmetries, such as $U(1)$ and lattice symmetries, the emergent anomalies imply (generalized) Luttinger theorems, relating Fermi surface volume to various topological responses. The corresponding topological responses are the charge density for $p=1$, Hall conductivity for $p=3$, and polarization for $p=2$. As a by-product of our results, we clarify exactly what is anomalous about the surface states of nodal line semimetals.

cond-mat.str-el↗

arXiv2018

Quantifying the Imaginarity of Quantum Mechanics

The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with density matrices that are real with respect to a fixed basis. This theory is closely related to the resource theory of coherence, as it is basis dependent, and the imaginary numbers appear in the off-diagonal elements of the density matrix. Unlike coherence however, the set of physically realizable free operations is identical to both completely resource non-generating operations, and stochastically resource non-generating operations. Moreover, the resource theory of imaginarity does not have a self-adjoint resource destroying map. After introducing and characterizing the free operations, we provide several measures of imaginarity, and give necessary and sufficient conditions for pure state transformations via physically consistent free operations in the single shot regime.

quant-ph↗