arXiv subjects

Jaan Oitmaa

Publications and source records attributed to Jaan Oitmaa.

At least 19 recordsLinked to original sources

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗

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)].

cond-mat.str-el↗

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗

arXiv2019

Quantum Lifshitz criticality in a frustrated two-dimensional XY model

Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY-model. Specifically, we show that, unlike the SU(2) symmetric Lifshitz case, in the XY-model the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the Neel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.

cond-mat.str-el↗

arXiv2018

Properties of the spin liquid phase in the vicinity of the Néel - Spin-Spiral Lifshitz transition in frustrated magnets

Three decades ago Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear Néel phase and a spin spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the Néel and spin spiral phases. In the present work, using field theory techniques, we study properties of this universal spin liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critical points, excitation spectra, and spin-spin correlations functions. We argue that the spin liquid in the vicinity of 2D Lifshitz point (LP) is similar to the gapped Haldane phase in integer-spin 1D chains. We also consider a specific example of a frustrated system with the spiral-Néel LP, the $J_1-J_3$ antiferromagnet on the square lattice that manifests the spin liquid behavior. We present numerical series expansion calculations for this model and compare results of the calculations with predictions of the developed field theory.

cond-mat.str-el↗

arXiv2018

Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.

cond-mat.str-el↗

arXiv2017

High temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high temperature series expansion study

We develop high temperature series expansions for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. Numerical results for uniform susceptibility, heat capacity and entropy as a function of temperature for different values of the Kitaev coupling $K$ and Heisenberg exachange coupling $J$ (with $|J|\le |K|$) are presented. These expansions show good convergence down to a temperature of a fraction of $K$ and in some cases down to $T=K/10$. In the Kitaev exchange dominated regime, the inverse susceptibility has a nearly linear temperature dependence over a wide temperature range. However, we show that already at temperatures $10$-times the Curie-Weiss temperature, the effective Curie-Weiss constant estimated from the data can be off by a factor of 2. We find that the magnitude of the heat capacity maximum at the short-range order peak, is substantially smaller for small $J/K$ than for $J$ of order or larger than $K$. We suggest that this itself represents a simple marker for the relative importance of the Kitaev terms in these systems. Somewhat surprisingly, both heat capacity and susceptibility data on Na$_2$IrO$_3$ are consistent with a dominant {\it antiferromagnetic} Kitaev exchange constant of about $300-400$ $K$.

cond-mat.str-el↗

arXiv2016

Spiral versus modulated collinear phases in the quantum ANNNH model

Motivated by the discovery of spiral and modulated collinear phases in several magnetic materials, we investigate the magnetic properties of Heisenberg spin S=1/2 antiferromagnets in 2 and 3 dimensions, with frustration arising from 2nd-neighbor couplings in one axial direction (the ANNNH model). Our results clearly demonstrate the presence of an incommensurate spiral phase at T=0 in 2 dimensions, extending to finite temperatures in 3 dimensions. The crossover between Néel and spiral order occurs at a value of the frustration parameter considerably above the classical value 0.25, a sign of substantial quantum fluctuations. We also investigate a possible modulated collinear phase with a wavelength of 4 lattice spacings, and find that it has substantially higher energy and hence is not realized in the model.

cond-mat.str-el↗

arXiv2015

Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study

We study the competition between $\sqrt{3} \times \sqrt{3}$ (RT3) and $q=0$ (Q0) magnetic orders in spin-one and spin-$3/2$ Kagome-lattice XXZ antiferromagnets with varying XY anisotropy parameter $Δ$, using series expansion methods. The Hamiltonian is split into two parts: an $H_0$ which favors the classical order in the desired pattern and an $H_1$, which is treated in perturbation theory by a series expansion. We find that the ground state energy series for the RT3 and Q0 phases are identical up to sixth order in the expansion, but ultimately a selection occurs, which depends on spin and the anisotropy $Δ$. Results for ground state energy and the magnetization are presented. These results are compared with recent spin-wave theory and coupled-cluster calculations. The series results for the phase diagram are close to the predictions of spin-wave theory. For the spin-one model at the Heisenberg point ($Δ=1$), our results are consistent with a vanishing order parameter, that is an absence of a magnetically ordered phase. We also develop series expansions for the ground state energy of the spin-one Heisenberg model in the trimerized phase. We find that the ground state energy in this phase is lower than those of magnetically ordered ones, supporting the existence of a spontaneously trimerized phase in this model.

cond-mat.str-el↗

arXiv2014

Phase diagram of the frustrated quantum-XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point

We study the nearest-neighbor exchange ($J_1$) and second-neighbor exchange ($J_2$) XY antiferromagnet on the honeycomb lattice using ground state series expansions around N{é}el, columnar and dimer phases. The conventional two-sublattice XY N{é}el order at small $J_2$ vanishes at $J_2/J_1=0.22\pm 0.01$ in agreement with results from Density Matrix Renormalization Group (DMRG) studies. Near the transition, we find evidence for an {\it approximate} emergent symmetry between XY and Ising degrees of freedom, namely the nearest-neighbor Ising and XY spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating XY and Ising orders. At still larger $J_2/J_1$ the columnar and dimer energies are found to be nearly degenerate. At even larger $J_2$ the columnar phase is obtained. The ground state energies in all three phases are in good agreement with the values found in the DMRG studies.

cond-mat.str-el↗

arXiv2013

Exact solution and high temperature series expansion study of the 1/5-th depleted square lattice Ising model

The critical behavior of the 1/5-depleted square-lattice Ising model with nearest neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field susceptibility. For the exact solution we employ a decoration transformation followed by a mapping to a staggered 8-vertex model. This yields a quartic equation for the critical coupling giving $K_{c} (\equivβJ_{c}) =0.695$. The series expansion for the susceptibility, to $\mathcal{O}(K^{18})$, when analyzed via standard Padé approximant methods gives an estimate of K$_{c}$, consistent with the exact solution result to at least four significant figures. The series expansion is also analyzed for the leading amplitude and subdominant terms.

cond-mat.stat-mech↗

arXiv2012

Fermi Surface Reconstruction by Dynamic Magnetic Fluctuations and Spin-Charge Separation Near an O(3) Quantum Critical Point

Stimulated by the small/large Fermi surface controversy in the cuprates we consider a small number of holes injected into the bilayer antiferromagnet. The system has an O(3) quantum critical point (QCP) separating the magnetically ordered and the magnetically disordered phases. We demonstrate that nearly critical quantum magnetic fluctuations can change the Fermi surface topology and also lead to spin charge separation (SCS) in two dimensions. We demonstrate that in the physically interesting regime there is a magnetically driven Lifshitz point (LP) inside the magnetically disordered phase. At the LP the topology of the hole Fermi surface is changed. The position of the LP, while being close to the position of the QCP is generally different. Dependent on the additional hole hopping integrals $t^{\prime}$ and $t^{\prime\prime}$, the LP can be located either in the magnetically ordered phase and/or in the magnetically disordered phase. We also demonstrate that in this regime the hole spin and charge necessarily separate when approaching the QCP. The considered model sheds light on generic problems concerning the physics of the cuprates.

cond-mat.supr-con↗

arXiv2012

Fermi Surface Reconstruction by Dynamic Magnetic Fluctuations

We demonstrate that nearly critical quantum magnetic fluctuations in strongly correlated electron systems can change the Fermi surface topology and also lead to spin charge separation (SCS) in two dimensions. To demonstrate these effects we consider a small number of holes injected into the bilayer antiferromagnet. The system has a quantum critical point (QCP) which separates magnetically ordered and disordered phases. We demonstrate that in the physically interesting regime there is a magnetically driven Lifshitz point (LP) inside the magnetically disordered phase. At the LP the topology of the hole Fermi surface is changed. We also demonstrate that in this regime the hole spin and charge necessarily separate when approaching the QCP. The considered model sheds light on generic problems concerning the physics of the cuprates.

cond-mat.supr-con↗

arXiv2012

Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point

We study the bipartite entanglement entropy of the two-dimensional (2D) transverse-field Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between sub-systems. Series extrapolations are used to extract subleading power laws and logarithmic singularities as the quantum critical point is approached. In 1D, we find excellent agreement with exact results as well as quantum Monte Carlo simulations. In 2D, we find compelling evidence that the entanglement at a corner is significantly different from a free boson field theory. These results demonstrate the power of the series expansion method for calculating entanglement entropy in interacting systems, a fact that will be particularly useful in future searches for exotic quantum criticality in models with and without the sign problem.

cond-mat.stat-mech↗