arXiv subjects

Chris Hooley

Publications and source records attributed to Chris Hooley.

9 recordsLinked to original sources

arXiv2026

Counting Edge Modes with the Higher Berry Curvature: A Bulk Topological Order Parameter for Quantum Spin Chains

We show that the higher Berry curvature (HBC) can be used to count the gapless edge modes created by an entanglement cut, and thus defines an integer-valued topological order parameter for quantum spin chains. Given an individual spin-chain Hamiltonian, we construct an extending family by interpolating to a reference product N\'eel state, and show that the integral of the HBC over this extension is equal to the ordinary Berry phase of half of the chain swept out in response to an \textit{infinitesimal} field. It thus counts the spin of the gapless edge modes exposed by the cut, and a change in its integer value signals a phase transition. We illustrate this with several examples: $S=1/2$, $S=1$, and $S=3/2$ spin-Peierls chains, which undergo `singlet flop' transitions between different patterns of dimerisation; the bilinear-biquadratic chain, which clarifies the connection to the strict symmetry-protected topological phases classification; and the staggered $J_1$--$J_2$ chain, which has both nearest-neighbour and third-neighbour patterns of singlets depending on the signs of the interactions.

cond-mat.str-el↗

arXiv2026

Kondo singlet from ferromagnetic coupling: an analog of Anderson-Morel superconductivity in the magnetic channel

We consider magnetic impurities coupled to a conduction sea via a fully isotropic ferromagnetic spin-exchange term, the strength of which depends on the conduction-electron modes involved in the scattering. In the single-impurity case we show both analytically and numerically that there exists a parameter regime in which the conventional Kondo effect develops at low temperatures, leading to a singlet ground state. In the case of a lattice of impurities, we show that this leads to a heavy Fermi liquid state that is energetically favored over magnetic ordering in a broad parameter range. We argue that these effects are analogs of Anderson-Morel superconductivity, and discuss routes to their experimental realization.

cond-mat.str-el↗

arXiv2025

A Generalised Haldane Map from the Matrix Product State Path Integral to the Critical Theory of the $J_1$-$J_2$ Chain

We study the $J_1$-$J_2$ spin-$1/2$ chain using a path integral constructed over matrix product states (MPS). By virtue of its non-trivial entanglement structure, the MPS ansatz captures the key phases of the model even at a semi-classical, saddle-point level, and, as a variational state, is in good agreement with the field theory obtained by abelian bosonisation. Going beyond the semi-classical level, we show that the MPS ansatz facilitates a physically-motivated derivation of the field theory of the critical phase: by carefully taking the continuum limit -- a generalisation of the Haldane map -- we recover from the MPS path integral a field theory with the correct topological term and emergent $SO(4)$ symmetry, constructively linking the microscopic states and topological field-theoretic structures. Moreover, the dimerisation transition is particularly clear in the MPS formulation -- an explicit dimerisation potential becomes relevant, gapping out the magnetic fluctuations.

cond-mat.str-el↗

arXiv2024

Transition between critical antiferromagnetic phases in the $J_1$-$J_2$ spin chain

The $J_1$-$J_2$ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations. We show in this Letter that there are, in fact, \textit{two} distinct critical antiferromagnetic phases, where the roles of the local dimer field and its dual field are interchanged: the `Affleck-Haldane' phase near the Heisenberg point $J_2 = 0$, where the dimer field that parametrises local singlet order is gapless and part of a joint $O(4)$ N\'eel-singlet order parameter; and the `Zirnbauer' phase which appears at sufficiently large ferromagnetic $J_2$, where the dimer field is gapped out and its \textit{dual} field -- the instanton density of the $O(3)$ N\'eel field -- is critical instead. The phases are so-named because each realises one of the competing pictures for how the $O(3)$ non-linear sigma model with a topological theta term renormalises to the $\mathfrak{\hat{su}}(2)_1$ Wess-Zumino-Witten model. We support these predictions with density matrix renormalisation group calculations.

cond-mat.stat-mech↗

arXiv2024

Magic angle of Sr$_2$RuO$_4$: Optimizing correlation-driven superconductivity

Understanding of unconventional superconductivity is crucial for engineering materials with specific order parameters or elevated superconducting transition temperatures. However, for many materials, the pairing mechanism and symmetry of the order parameter remain unclear: reliable and efficient methods of predicting the order parameter and its response to tuning parameters are lacking. Here, we investigate the response of superconductivity in Sr$_2$RuO$_4$ to structural distortions via the random phase approximation (RPA) and functional renormalization group (FRG), starting from realistic models of the electronic structure. Our results suggest that RPA misses the interplay of competing fluctuation channels. FRG reproduces key experimental findings. We predict a magic octahedral rotation angle, maximizing the superconducting $T_c$ and a dominant $d_{x^2-y^2}$ pairing symmetry. To enable experimental verification, we provide calculations of the phase-referenced Bogoliubov Quasiparticle Interference imaging. Our work demonstrates a designer approach to tuning unconventional superconductivity with relevance and applicability for a wide range of quantum materials.

cond-mat.supr-con↗

arXiv2024

Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems

Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit reset. The possibility of realizing discrete-time reset dynamics on quantum computers makes it important to investigate the steady-state properties of such dynamics. Here, we explore the behavior of generic discrete-time unitary dynamics interspersed by random reset events. For Poissonian resets, we compute the stationary state of the process and demonstrate, by taking a weak-reset limit, the existence of "resonances" in the quantum gates, allowing for the emergence of steady state density matrices which are not diagonal in the eigenbasis of the generator of the unitary gate. Such resonances are a genuine discrete-time feature and impact on quantum and classical correlations even beyond the weak-reset limit. Furthermore, we consider non-Poissonian reset processes and explore conditions for the existence of a steady state. We show that, when the reset probability vanishes sufficiently rapidly with time, the system does not approach a steady state. Our results highlight key differences between continuous-time and discrete-time stochastic resetting and may be useful to engineer states with controllable correlations on existing devices.

quant-ph↗

arXiv2024

Origin of the intermediate-temperature magnetic specific heat capacity in the spin-liquid candidate Ca$_{10}$Cr$_7$O$_{28}$

We present several approximate calculations of the specific heat capacity of the model for Ca$_{10}$Cr$_7$O$_{28}$ proposed by Balz et al. [Phys. Rev. B 95, 174414 (2017)], using methods including exact diagonalization, Thermal Pure Quantum States, and high-temperature expansions. In none of these cases are we able to reproduce the magnitude of the zero-field specific heat capacity shown in the intermediate-temperature $({\sim}\,5-15\,\rm{K})$ experimental data. We discuss possible reasons for the discrepancy, and what it might tell us about the magnetic Hamiltonian for Ca$_{10}$Cr$_7$O$_{28}$.

cond-mat.str-el↗

arXiv2018

Can Topological Transitions be Exploited to Engineer Intrinsically Quench-resistant Wires?

We investigate whether by synthesising superconductors that are tuned to a topological, node-reconstruction transition point we could create superconducting wires that are intrinsically resilient to quenches. Recent work shows that the exponent characterising the temperature dependence of the specific heat of a nodal superconductor is lowered over a region of the phase diagram near topological transitions where nodal lines form or reconnect. Our idea is that the resulting enhancement of the low-temperature specific heat could have potential application in the prevention of superconductor quenches. We perform numerical simulations of a simplified superconductor quench model. Results show that decreasing the specific heat exponent can prevent a quench from occurring and improve quench resilience, though in our simple model the effects are small. Further work will be necessary to establish the practical feasibility of this approach.

cond-mat.supr-con↗

arXiv2007

Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling

We propose an experiment to obtain the phase diagram of the fermionic Hubbard model, for any dimensionality, using cold atoms in optical lattices. It is based on measuring the total energy for a sequence of trap profiles. It combines finite-size scaling with an additional `finite-curvature scaling' necessary to reach the homogeneous limit. We illustrate its viability in the 1D case, simulating experimental data in the Bethe-Ansatz local density approximation. Including experimental errors, the filling corresponding to the Mott transition can be determined with better than 3% accuracy.

cond-mat.other↗