arXiv subjects

Rajiv R. P. Singh

Publications and source records attributed to Rajiv R. P. Singh.

At least 19 recordsLinked to original sources

arXiv2026

A long-range model for the electron-nuclear coupling and two-stage order in TmVO$_4$

We study an infinite-range coupled electronic-quadrupole and nuclear-spin model for ferro-quadrupolar and nuclear-spin ordering in TmVO$_4$ in external magnetic and strain fields. This material is an experimental realization of a Transverse-Field Ising Model, where the Ising degree of freedom is quadrupolar and non-magnetic, but a transverse component is magnetic and couples both to external magnetic fields and to the nuclear spins via a hyperfine coupling. In zero external magnetic-field, there is a well-separated two-step order of the electronic and nuclear degrees of freedom and the release of their respective entropies. A transverse magnetic-field polarizes the electronic orbital moments and also the nuclear spins via the hyperfine coupling. The quadrupolar ordering temperature is gradually reduced to zero. But, there is no longer a nuclear transition in non-zero fields. Quantum fluctuations are magnified near the phase transitions and lead to peaks in the magnetic susceptibility. The spectral functions reveal a softening of a low-energy mode near the quantum critical point, consistent with the closing of the excitation gap and its reopening in the disordered phase, providing direct dynamical signatures of the field-driven quantum critical phenomena.

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arXiv2024

Frustrated spin-1/2 Heisenberg model on a Kagome-strip chain: Dimerization and mapping to a spin-orbital Kugel-Khomskii model

We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a Kagome-strip chain (KSC), a one-dimensional analogue of the Kagome lattice, and construct its phase diagram in an extended exchange parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-$3/2$ state as well as spin-$1/2$ states with and without additional degeneracies. We explore the ground state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.

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arXiv2024

Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores

Gauge theories are powerful tools in theoretical physics, allowing complex phenomena to be reduced to simple principles, and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behaviour at zero temperature but crucially determine the system's temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and matrix gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the matrix gauge field, rendering the system spin ice like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and matrix gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers pyrochlore materials.

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arXiv2024

Quantum Criticality in the infinite-range Transverse Field Ising Model

We study quantum criticality in the infinite range Transverse-Field Ising Model. We find subtle differences with respect to the well-known single-site mean-field theory, especially in terms of gap, entanglement and quantum criticality. The calculations are based on numerical diagonalization of Hamiltonians with up to a few thousand spins. This is made possible by the enhanced symmetries of the model, which divide the Hamiltonian into many block-diagonal sectors. The finite temperature phase diagram and the characteristic jump in heat capacity closely resemble the behavior in mean-field theory. However, unlike mean-field theory where excitations are always gapped, the excitation gap in the infinite range model goes to zero from both the paramagnetic side and from the ferromagnetic side on approach to the quantum critical point. Also, contrary to mean-field theory, at the quantum critical point the Quantum Fisher Information becomes large, implying long-range multi-partite entanglement. We find that the main role of temperature is to shift statistical weights from one conserved sector to another. However, low energy excitations in each sector arise only near the quantum critical point implying that low energy quantum fluctuations can arise only in the vicinity of the quantum critical field where they can persist up to temperatures of order the exchange constant.

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arXiv2023

Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions

We investigate the ground state and critical temperature phase diagrams of the classical and quantum $S=1/2$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered $XY$ phase, known as $Γ_5$, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the $ψ_3$ state in most parts of the $Γ_5$ regime. Likewise, thermal fluctuations treated classically, select the $ψ_3$ state at $T=0^+$. In contrast, classical Monte Carlo finds that the system orders at $T_c$ in the $ψ_2$ state of $Γ_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from $ψ_2$ to $ψ_3$ at a temperature $T_{Γ_5} <T_c$. The same method finds that the system orders via a single transition at $T_c$ directly into the $ψ_3$ state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at $T_c$ for the $S=1/2$ quantum model is corroborated by high-temperature series expansion. To investigate the $T=0$ quantum ground states, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic $S=1/2$ Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. We find that near the boundary of ferromagnetism and $Γ_5$ antiferromagnetism the system may potentially realize a quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same ordered phases as in the classical model.

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arXiv2023

High-temperature magnetization and entropy of the triangular lattice Hubbard model in a Zeeman field

We use strong coupling expansions to calculate the entropy function $S(T,h)$, the magnetization $M(T,h)$, and the double occupancy factor $D(T,h)$ for the half-filled triangular lattice Hubbard model as a function of temperature $T$ and Zeeman field $h$, for various values of the Hubbard parameter ratio $U/t$. These calculations converge well for temperatures larger than the exchange parameter $J=\frac{4t^2}{U}$ for moderate to large $U/t$ values. Setting $μ=U/2$ suffices to obtain the density of half filling within a fraction of one percent at all temperatures studied for $U/t \geq 8$. We discuss the systematic variation of properties with $U/t$. The temperature dependence of entropy and the double occupancy parameter shows a mapping to an antiferromagnetic Mott insulating behavior at temperatures well above $T=J$ for $U/t\ge 10$. Convergence of the series is weaker at intermediate fields implying non-monotonic variation of spin-correlations with the Zeeman field. We discuss the relevance of the Hubbard model results to the triangular-lattice antiferromagnetic materials Lu$_3$Cu$_2$Sb$_3$O$_{14} $ (LCSO) studied recently by Yang et al [Yang et al arXiv:2102.09271 (2022)].

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arXiv2022

Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies

We study the spin-one Kitaev model on the honeycomb lattice in the presence of single-ion anisotropies. We consider two types of single ion anisotropies: A $D_{111}$ anisotropy which preserves the symmetry between $X$, $Y$, and $Z$ bonds but violates flux conservation and a $D_{100}$ anisotropy that breaks the symmetry between $X$, $Y$, and $Z$ bonds but preserves flux conservation. We use series expansion methods, degenerate perturbation theory, and exact diagonalization to study these systems. Large positive $D_{111}$ anisotropy leads to a simple product ground state with conventional magnon-like excitations, while large negative $D_{111}$ leads to a broken symmetry and degenerate ground states. For both signs there is a phase transition at a small $|D_{111}| \approx 0.12$ separating the more conventional phases from the Kitaev spin liquid phase. With large $D_{100}$ anisotropy, the ground state is a simple product state, but the model lacks conventional dispersive excitations due to the large number of conservation laws. Large negative $D_{100}$ leads to decoupled one-dimensional systems and many degenerate ground states. No evidence of a phase transition is seen in our numerical studies at any finite $D_{100}$. Convergence of the series expansion extrapolations all the way to $D_{100}=0$ suggests that the nontrivial Kitaev spin liquid is a singular limit of this type of single-ion anisotropy going to zero, which also restores symmetry between the $X$, $Y$, and $Z$ bonds.

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arXiv2022

Onset of charge incompressibility and Mott gaps in the Honeycomb-Lattice SU(4) Hubbard Model: Lessons for Twisted Bilayer Graphene systems

We use finite temperature strong coupling expansions to calculate thermodynamic properties of the Honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in t/U. We discuss lessons that can be drawn from high temperature properties of a simple Hubbard model regarding Twisted Bilayer Graphene (TBG) and other magic-angle flat-band systems.

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arXiv2022

Order, Disorder and Monopole Confinement in the Spin-$1/2$ XXZ Model on a Pyrochlore Tube

We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction $J_z$ and a transverse exchange interaction $J_{x}$, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When $J_z$ is antiferromagnetic ($J_{z}>0$) and $J_x$ is ferromagnetic ($J_{x}<0$), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at $T=0$. For $J_{z}<0$ and $J_{x}>0$, spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a non-degenerate ground state with no broken symmetries and a robust energy gap. The low energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small $|J_{x}|$, we study the confinement of monopole-anti-monopole pairs and find that the confinement length scale is larger for $J_x<0$ than for $J_{x}>0$, although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.

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arXiv2022

On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet

Using finite temperature strong coupling expansions for the SU(N) Hubbard Model, we calculate the thermodynamic properties of the model in the infinite-$U$ limit for arbitrary density $0\leq ρ\leq 1$ and all $N$. We express the ferromagnetic susceptibility of the model as a Curie term plus a $Δχ$, an excess susceptibility above the Curie-behavior. We show that, on a bipartite lattice, graph by graph the contributions to $Δχ$ are non-negative in the limit that the hole density $δ=1-ρ$ goes to zero. By summing the contributions from all graphs consisting of closed loops we find that the low hole-density ferromagnetic susceptibility diverges exponentially as $\exp{Δ/T}$ as $T \to 0$ in two and higher dimensions. This demonstrates that Nagaoka-Thouless ferromagnetic state exists as a thermodynamic state of matter at low enough density of holes and sufficiently low temperatures. The constant $Δ$ scales with the SU(N) parameter $N$ as $1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as the characteristic temperature scale for ferromagnetic order goes down.

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arXiv2022

Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model

We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of $βt$, $w=\exp{(-βU)}$ and ${1\over βU}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for $U$ larger than or of order the Bandwidth, the expansions converge over a wide temperature range $t^2/U \ \lesssim \ T \ \lesssim \ 10 U$. By taking the limit $w\to 0$, valid at temperatures much less than $U$, the expansions turn into a high temperature expansion for a dressed SU(N) Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges and ring exchanges known from the $T=0$ perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\to 0$ limit corresponds to an effective $t-J$ model. The onset of strong correlations can be identified by a plateau-like behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $δ=1-n$, the deviation from one particle per site, where the leading $βt$ dependent terms correspond to holes sloshing around in a disordered SU(N) background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.

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arXiv2021

Magnetism of competing high-spin/low-spin states in Ba$_2$NiO$_2$(AgSe)$_2$ and related two-orbital two-electron systems

We discuss the thermodynamic and magnetic properties of a competing high-spin/low-spin two-orbital two-electron model on a square-lattice possibly relevant to the nickelates such as Ba$_2$NiO$_2$(AgSe)$_2$ (BNOAS). We focus on parameter regimes where a high-spin ($S=1$) and a low-spin ($S=0$) state are energetically close to each other and discuss various exchange processes in such a system. The model we study is a variant of, but different from the Kondo-necklace model proposed for the system by Jin et al (H. S. Jin, W. E. Pickett and K. W. Lee, Phys. Rev. Research 2, 033197 (2020)). Although there are similarities between the two models in terms of the ground-state phases and their symmetries, the detailed properties of the different phases and the phase transitions are entirely different and should be easy to distinguish from an experimental point of view.

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arXiv2021

Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice

We study the thermodynamic properties of modified spin-$S$ Kitaev models introduced by Baskaran, Sen and Shankar (Phys. Rev. B 78, 115116 (2008)). These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high temperature expansions and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin $S=1$ and $S=2$. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as $T\to 0$, become critical as $T\to 0$ or diverge exponentially as $T\to 0$. There is a conserved $Z_2$ flux variable associated with each hexagonal plaquette which saturates at the value $+1$ as $T\rightarrow0$ in all models except the $S=1$ antiferromagnet where the mean flux remains zero as $T\to 0$. We provide qualitative explanations for these results.

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arXiv2020

On two phases inside the Bose condensation dome of Yb$_2$Si$_2$O$_7$

Recent experimental data on Bose-Einstein Condensation (BEC) of magnons in the spin-gap compound Yb$_2$Si$_2$O$_7$ revealed an asymmetric BEC dome arXiv:1810.13096v2. We examine modifications to the Heisenberg model on a breathing honeycomb lattice, showing that this physics can be explained by competing forms of weak anisotropy. We employ a gamut of analytical and numerical techniques to show that the anisotropy yields a field driven phase transition from a state with broken Ising symmetry to a phase which breaks no symmetries and crosses over to the polarized limit.

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arXiv2020

High-Field Expansion Approach to Kagome Antiferromagnets with Dzyaloshinskii-Moriya Interactions

We apply linked cluster expansion techniques to study the polarized high-field phase of a spin-half antiferromagnet on the Kagome lattice with Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We find that the Dirac points of the single-magnon spectrum without DMI are robust against arbitrary DMI when the magnetic field lies in the Kagome plane. Unlike the typical case where DMI gaps the spectrum, here we find that varying the DMI merely shifts the location of the Dirac points. In contrast, a magnetic field with a component out of the Kagome plane gaps the spectrum, leading to topological magnon bands. We map out a topological phase diagram as the couplings are varied by computing the band Chern numbers. A pair of phase transitions are observed and we find an enhanced thermal Hall conductivity near the phase boundary.

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arXiv2019

Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

We study an effective spin model derived perturbatively from random transverse-field Ising model on the pyrochlore lattice. The model consists of spin-configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization upto N=64 site systems. We calculate spin-glass correlation functions and local entanglement entropy $S_T$ between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where $S_T=\ln{6}$. Increasing randomness first leads to a frozen phase, with long-range spin-glass order and $S_T=\ln{2}$ corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

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arXiv2019

Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets

Residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-$Z_2$-flux variables in Kitaev models, the freezing of one set of degrees of freedom and establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO$_4$ by Li et al, we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. We find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.

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arXiv2019

Rapid filling of the spin gap with temperature in the Schwinger-boson mean-field theory of the antiferromagnetic Heisenberg kagome model

Using Schwinger-boson mean-field theory, we calculate the dynamic spin structure factor at low temperatures $0<T\ll J$ for the spin-$1/2$ antiferromagnetic Heisenberg kagome model, within the gapped $\mathbb{Z}_2$ spin liquid phase Ansatz. We find that the spectral gap rapidly fills with temperature, with robust low-energy spectral weight developing by a temperature of $Δ/3$, where the spin gap is $2Δ$ (i.e., $Δ$ is the spinon gap), before any appreciable rise in spinon density or change in zero-temperature mean-field parameters. This is due to deconfinement of spinons which leads to terms suppressed only by $\exp(-Δ/T)$. At still higher temperatures, the spinon density increases rapidly leading to a breakdown of the Schwinger-boson mean-field approach. We suggest that if the impurity-free spectral functions can be obtained through neutron scattering experiments on kagome herbertsmithites, temperature dependence of the subgap weight can provide distinct signatures of a $\mathbb{Z}_2$ quantum spin liquid.

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