arXiv subjects

Ross H. McKenzie

Publications and source records attributed to Ross H. McKenzie.

At least 19 recordsLinked to original sources

arXiv2026

Exact mapping from short-ranged harmonic elastic models of spin crossover materials to Ising models with interactions at all length scales

Spin crossover (SCO) materials are reversible molecular switches found in a wide range of transition metal complexes and metal organic frameworks (MOFs). They exhibit diverse spin state orderings and transitions between them. Here we present an exact mapping from harmonic elastic models to Ising-like models with both a short-range Ising interaction that decays with a power law at large distances and a long-range (infinite-range) Husimi-Temperley interaction that is independent of distance. We apply this mapping to a simple model of SCO frameworks. This provides a microscopic justification for an Ising-Husimi-Temperley model description, which has previously only been justified on phenomenological grounds. Elastic frustration is required for non-zero Ising interactions, but whether or not the short-range interactions in the Ising model are geometrically frustrated depends on the ratio of the bulk and shear moduli, or equivalently Poisson's ratio. The long-range interaction has two origins: (i) a self-interaction on the average spin state, mediated through the coupling between the average spin state and the unit cell parameters; and (ii) an infrared divergence in the spin state-spin state coupling mediated by displacements of metals and ligands within the unit cell. %In the absence of elastic frustration these terms are equal and opposite so there is no long-range interaction. However, in general they do not cancel and there is a long-range Ising interaction. The long-range interaction is independent of the distance between metal centers, nevertheless it leads to an extensive contribution to the (free) energy. In this model the Husimi-Temperley interaction dominates transitions of spin states, whereas multistep transitions and intermediate order are observed if only the pure (power-law) Ising interaction are retained, only single-step transitions are found in the full model.

cond-mat.str-el↗

arXiv2026

Emergence: from physics to biology, sociology, and computer science

Many systems involve numerous interacting parts and the whole system can have properties that the individual parts do not. I take this novelty as the defining characteristic of an emergent property. Other characteristics associated with emergence discussed include universality, order, complexity, unpredictability, irreducibility, diversity, self-organisation, discontinuities, and singularities. Emergent phenomena are widespread across physics, biology, social sciences, and computing, and are central to major scientific and societal challenges. Understanding emergence involves considering the stratification of reality across different scales (energy, time, length, complexity), each with its distinct ontology and epistemology, leading to semi-autonomous scientific disciplines. A central challenge is bridging the gap between macroscopic emergent properties and microscopic component interactions. Identifying an intermediate mesoscopic scale where new, weakly interacting entities or modular structures emerge is key. Theoretical approaches, such as effective theories (describing phenomena at a specific scale) and toy models (simplified systems for analysis), are vital. The Ising model exemplifies how toy models can elucidate emergence characteristics. Emergence is central to condensed matter physics, chaotic systems, fluid dynamics, nuclear physics, quantum gravity, neural networks, protein folding, and social segregation. An emergent perspective should influence scientific strategy by shaping research questions, methodologies, priorities, and resource allocation. An elusive goal is the design and control of emergent properties.

physics.hist-ph↗

arXiv2022

$C_3$ symmetry breaking metal-insulator transitions in a flat band in the half-filled Hubbard model on the decorated honeycomb lattice

We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the non-interacting theory at half-filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states - a dimer valence bond solid Mott insulator when inter-triangle correlations dominate, and a broken $\mathcal{C}_3$-symmetry antiferromagnet that arises from frustration when intra-triangle correlations dominate. The metal-insulator transitions into these two phases have very different characters. The metal-broken $\mathcal{C}_3$ antiferromagnetic transition is driven by spontaneous $\mathcal{C}_3$ symmetry breaking that lifts the topologically required degeneracy at the Fermi energy and opens an energy gap in the quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no symmetries of the Hamiltonian. It is caused by strong correlations renormalizing the electronic structure into a phase that is adiabatically connected to both the trivial band insulator and the ground state of the spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither of these metal-insulator transitions can be understood in either the Brinkmann-Rice or Slater paradigms.

cond-mat.str-el↗

arXiv2021

Spin-$0$ Mott insulator to metal to spin-$1$ Mott insulator transition in the single-orbital Hubbard model on the decorated honeycomb lattice

We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenough-Kanamori rules, may occur in coordination polymers from kinetic exchange via the ligands. We characterize the magnetism in the regime where spin-triplets dominate. For small $U$ a spin-$1$ Slater insulator occurs with antiferromagnetic order between triangles. Magnetism in the spin-$1$ Mott insulator is described by a spin-$1$ Heisenberg model on a honeycomb lattice, whose ground state is Néel ordered.

cond-mat.str-el↗

arXiv2021

Multiple insulating phases due to the interplay of strong correlations and lattice geometry in a single-orbital Hubbard model

We report ten ground states arising from strong correlations in the single-orbital Hubbard model on the decorated honeycomb lattice; including Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and trimer Mott insulators, and a spin-$1$ Mott insulator. The rich phase diagram arises from structures within the unit cell. Hence, such states are absent on simpler lattices. We argue that such insulating phases are prevalent on decorated lattices. These are found in many materials and common in coordination polymers, providing a playground to explore this physics.

cond-mat.str-el↗

arXiv2019

Orbital-selective bad metals due to Hund's rule and orbital anisotropy: a finite-temperature slave-spin treatment of the two-band Hubbard model

We study the finite-temperature properties of the half-filled two-band Hubbard model in the presence of Hund's rule coupling and orbital anisotropy. We use the mean-field treatment of the $Z_2$ slave-spin theory with a finite-temperature extension of the zero-temperature gauge variable previously developed by Hassan and de' Medici http://dx.doi.org/10.1103/PhysRevB.81.035106}{Phys. Rev. B {\bf 81}, 035106 (2010)}]. We consider the instability of the Fermi liquid phases and how it is enhanced by the Hund's rule. We identify paramagnetic solutions that have zero quasi-particle weight with bad metallic phases, and the first-order transition temperature between it and the Fermi liquid phase as a coherence temperature that signals the crossover to the bad metallic state. When orbital anisotropy is present, we found an intermediate transition to an orbital-selective bad metal (OSBM), where the narrow band becomes a bad metal while the wide band remains a renormalised Fermi liquid. The temperatures $T_\textrm{coh}$ and $T_\textrm{OSBM}$ at which the system transitions to the bad metal phases can be orders of magnitude less than the Fermi temperature associated with the non-interacting band. The parameter dependence of the temperature at which the OSBM is destroyed can be understood in terms of a ferromagnetic Kondo-Hubbard lattice model. In general, Hund's rule coupling enhances the bad metallic phases, reduce interorbital charge fluctuations and increase spin fluctuations. The qualitative difference found in the ground state whether the Hund's rule is present or not, related to the degeneracy of the low energy manifold, is also maintained for finite temperatures.

cond-mat.str-el↗

arXiv2017

Low quasiparticle coherence temperature in the one band-Hubbard model: A slave-boson approach

We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight $Z$ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature $T_\textrm{coh}$ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as a function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with Dynamical Mean-Field Theory. We analyse the stability of the method by calculating the charge compressibility.

cond-mat.str-el↗

arXiv2017

Quantum critical local spin dynamics near the Mott metal-insulator transition in infinite dimensions

Finding microscopic models for metallic states that exhibit quantum critical properties such as $ω/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $χ(T,ω)$ for a Hubbard model at half filling using Dynamical Mean-Field Theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite temperature critical point. The signature of the latter is $ω/T$ scaling where $T$ is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity and are relevant to experiments on organic charge transfer salts.

cond-mat.str-el↗

arXiv2016

Effect of hydrogen bonding on infrared absorption intensity

We consider how the infrared intensity of an O-H stretch in a hydrogen bonded complex varies as the strength of the H-bond varies from weak to strong. We obtain trends for the fundamental and overtone transitions as a function of donor-acceptor distance R, which is a common measure of H-bond strength. Our calculations use a simple two-diabatic state model that permits symmetric and asymmetric bonds, i.e. where the proton affinity of the donor and acceptor are equal and unequal, respectively. The dipole moment function uses a Mecke form for the free OH dipole moment, associated with the diabatic states. The transition dipole moment is calculated using one-dimensional vibrational eigenstates associated with the H-atom transfer coordinate on the ground state adiabatic surface of our model. Over 20-fold intensity enhancements for the fundamental are found for strong H-bonds, where there are significant non-Condon effects. The isotope effect on the intensity yields a non-monotonic H/D intensity ratio as a function of R, and is enhanced by the secondary geometric isotope effect. The first overtone intensity is found to vary non-monotonically with H-bond strength; strong enhancements are possible for strong H-bonds. Modifying the dipole moment through the Mecke parameters is found to have a stronger effect on the overtone than the fundamental. We compare our findings with those for specific molecular systems analysed through experiments and theory in earlier works. Our model results compare favourably for strong and medium strength symmetric H-bonds. However, for weak asymmetric bonds we find much smaller effects than in earlier work.

physics.chem-ph↗

arXiv2016

Spin-orbit coupling and odd-parity superconductivity in the quasi-one-dimensional compound Li$_{0.9}$Mo$_6$O$_{17}$

Previous theoretical studies [W. Cho, C. Platt, R. H. McKenzie, and S. Raghu, Phys. Rev. B 92, 134514 (2015); N. Lera and J. V. Alvarez, Phys. Rev. B 92, 174523 (2015)] have suggested that Li$_{0.9}$Mo$_6$O$_{17}$, a quasi-one dimensional "purple bronze" compound, exhibits spin-triplet superconductivity and that the gap function changes sign across the two nearly degenerate Fermi surface sheets. We investigate the role of spin-orbit coupling (SOC) in determining the symmetry and orientation of the $d$-vector associated with the superconducting order parameter. We propose that the lack of local inversion symmetry within the four-atom unit cell leads to a staggered spin-orbit coupling analogous to that proposed for graphene, MoS$_2$, or SrPtAs. In addition, from a weak-coupling renormalization group treatment of an effective model Hamiltonian, we find that SOC favors the odd parity $A_{1u}$ state with $S_z = \pm 1$ over the $B$ states with $S_z=0$, where $z$ denotes the least-conducting direction. We discuss possible definitive experimental signatures of this superconducting state.

cond-mat.supr-con↗

arXiv2015

Holon-Doublon Binding as the Mechanism for the Mott transition

We study the binding of a holon to a doublon in a half-filled Hubbard model as the mechanism of the zero-temperature metal-insulator transition. In a spin polarized system and a non-bipartite lattice a single holon-doublon (HD) pair exhibits a binding transition (e.g., on a face-centred cubic lattice), or a sharp crossover (e.g., on a triangular lattice) corresponding well to the standard Mott transition in unpolarized systems. We extend the HD-pair study towards non-polarized systems by considering more general spin background and by treating the finite HD density within a BCS-type approximation. Both approaches lead to a discontinuous transition away from the fully polarized system and give density correlations consistent with numerical results on a triangular lattice.

cond-mat.str-el↗

arXiv2015

Spin-triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound Li$_{0.9}$Mo$_6$O$_{17}$

The purple bronze Li$_{0.9}$Mo$_6$O$_{17}$ is of interest due to its quasi-one-dimensional electronic structure and the possible Luttinger liquid behavior resulting from it. For sufficiently low temperatures, it is a superconductor with a pairing symmetry that is still to be determined. To shed light on this issue, we analyze a minimal Hubbard model for this material involving four molybdenum orbitals per unit cell near quarter filling, using asymptotically exact perturbative renormalization group methods. We find that spin triplet odd-parity superconductivity is the dominant instability. Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces enhance certain second-order processes, which play crucial roles in determining the structure of the pairing gap. Notably, we find that the gap has accidental nodes, i.e. it has more sign changes than required by the point-group symmetry.

cond-mat.supr-con↗

arXiv2015

Shear viscosity of strongly interacting fermionic quantum fluids

Eighty years ago Eyring proposed that the shear viscosity of a liquid, $η$, has a quantum limit $η\gtrsim n\hbar$ where $n$ is the density of the fluid. Using holographic duality and the AdS/CFT correspondence in string theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound $\fracη{s}\geq \frac{\hbar}{4πk_{B}}$ for the ratio between the shear viscosity and the entropy density, $s$. Using Dynamical Mean-Field Theory (DMFT) we calculate the shear viscosity and entropy density for a fermionic fluid described by a single band Hubbard model at half filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid $^{3}$He. At low temperature the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid $1/T^{2}$ dependence, where $T$ is the temperature. With increasing temperature and interaction strength $U$ there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasi-particle based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid $^{3}$He. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge transfer salts.

cond-mat.str-el↗

arXiv2015

Isotopic fractionation in proteins as a measure of hydrogen bond length

If a deuterated molecule containing strong intramolecular hydrogen bonds is placed in a hydrogenated solvent it may preferentially exchange deuterium for hydrogen. This preference is due to the difference between the vibrational zero-point energy for hydrogen and deuterium. It is found that the associated fractionation factor $Φ$ is correlated with the strength of the intramolecular hydrogen bonds. This correlation has been used to determine the length of the H-bonds (donor-acceptor separation) in a diverse range of enzymes and has been argued to support the existence of short low-barrier H-bonds. Starting with a potential energy surface based on a simple diabatic state model for H-bonds we calculate $Φ$ as a function of the proton donor-acceptor distance $R$. For numerical results, we use a parameterization of the model for symmetric O-H.... O bonds. We consider the relative contributions of the O-H stretch vibration, O-H bend vibrations (both in plane and out of plane), tunnelling splitting effects at finite temperature, and the secondary geometric isotope effect. We compare our total $Φ$ as a function of $R$ with NMR experimental results for enzymes, and in particular with an empirical parametrisation $Φ(R)$, used previously to determine bond lengths.

physics.chem-ph↗

arXiv2015

Absence of a quantum limit to charge diffusion in bad metals

Good metals are characterised by diffusive transport of coherent quasi-particle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit, $\frac{ha}{e^{2}}$, where $a$ is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge diffusion constant, $D \gtrsim \hbar v_{F}^{2}/(k_{B}T)$, in the incoherent regime of transport, where $v_F$ is the Fermi velocity and $T$ the temperature. Using dynamical mean field theory (DMFT) we calculate the charge diffusion constant in a single band Hubbard model at half filling. We show that in the strongly correlated regime the Hartnoll's bound is violated in the crossover region between the coherent Fermi liquid region and the incoherent (bad metal) local moment region. The violation occurs even when the bare Fermi velocity $v_F$ is replaced by its low temperature renormalised value, $v_F^*$.The bound is satisfied at all temperatures in the weakly and moderately correlated systems as well as in strongly correlated systems in the high temperature region where the resistivity is close to linear in temperature. Our calculated charge diffusion constant, in the incoherent regime of transport, also strongly violates a proposed quantum limit of spin diffusion, $D_{s} \sim 1.3 \hbar/m$, where $m$ is the fermion mass, experimentally observed and theoretically calculated in a cold degenerate Fermi gas in the unitary limit of scattering.

cond-mat.str-el↗

arXiv2015

Valence-bond Non-equilibrium Solvation Model for a Twisting Monomethine Cyanine

We propose and analyze a two-state valence-bond model of non-equilibrium solvation effects on the excited-state twisting reaction of monomethine cyanines. Suppression of this reaction is thought responsible for environment-dependent fluorescence yield enhancement in these dyes. Fluorescence is quenched because twisting is accompanied via the formation of dark twisted intramolecular charge-transfer (TICT) states. For monomethine cyanines, where the ground state is a superposition of structures with different bond and charge localization, there are two possible twisting pathways with different charge localization in the excited state. For parameters corresponding to symmetric monomethines, the model predicts two low-energy twisting channels on the excited-state surface that lead to a manifold of twisted intramolecular charge-transfer (TICT) states. For typical monomethines, twisting on the excited state surface will occur with a small barrier or no barrier. Changes in the solvation configuration can differentially stabilize TICT states in channels corresponding to different bonds, and that the position of a conical intersection between adiabatic states moves in response to solvation to stabilize either one channel or the other. There is a conical intersection seam that grows along the bottom of the excited-state potential with increasing solvent polarity. For monomethine cyanines with modest-sized terminal groups in moderately polar solution, the bottom of the excited-state potential surface is completely spanned by a conical intersection seam.

physics.chem-ph↗

arXiv2014

Enhancement of the thermal expansion of organic charge transfer salts by strong electronic correlations

Organic charge transfer salts exhibit thermal expansion anomalies similar to those found in other strongly correlated electron systems. The thermal expansion can be anisotropic and have a non-monotonic temperature dependence. We show how these anomalies can arise from electronic effects and be significantly enhanced, particularly at temperatures below 100 K, by strong electronic correlations. For the relevant Hubbard model the thermal expansion is related to the dependence of the entropy on the parameters ($t$, $t'$, and $U$) in the Hamiltonian or the temperature dependence of bond orders and double occupancy. The latter are calculated on finite lattices with the Finite Temperature Lanczos Method. Although many features seen in experimental data, in both the metallic and Mott insulating phase, are described qualitatively, the calculated magnitude of the thermal expansion is smaller than that observed experimentally.

cond-mat.str-el↗

arXiv2014

A diabatic state model for double proton transfer in hydrogen bonded complexes

Four diabatic states are used to construct a simple model for double proton transfer in hydrogen bonded complexes. Key parameters in the model are the proton donor-acceptor separation R and the ratio, D_1/D_2, between the proton affinity of a donor with one and two protons. Depending on the values of these two parameters the model describes four qualitatively different ground state potential energy surfaces, having zero, one, two, or four saddle points. In the limit D_2=D_1 the model reduces to two decoupled hydrogen bonds. As R decreases a transition can occur from a concerted to a sequential mechanism for double proton transfer.

physics.chem-ph↗