arXiv subjects

R. T. Scalettar

Publications and source records attributed to R. T. Scalettar.

At least 19 recordsLinked to original sources

arXiv2024

Supersolid Phase in the Diluted Holstein Model

The Holstein model on a square lattice at half-filling has a well-established finite temperature phase transition to an insulating state with long range charge density wave (CDW) order. Because this CDW formation suppresses pairing, a superconducting (SC) phase emerges only with doping. In this work, we study the effects of dilution of the local phonon degrees of freedom in the Holstein model while keeping the system at half filling. We find not only that the CDW remains present up to a dilution fraction $f \sim 0.15$, but also that long range pairing is stabilized with increasing $f$, resulting in a {\it supersolid} regime centered at $f \approx 0.10$, where long range diagonal and off-diagonal correlations coexist. Further dilution results in a purely SC phase, and ultimately in a normal metal. Our results provide a new route to the supersolid phase via the introduction of impurities at fixed positions which both increase quantum fluctuations and also are immune to the competing tendency to phase separation often observed in the doped case.

cond-mat.str-el↗

arXiv2023

Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential

The Holstein Hamiltonian describes itinerant electrons whose site density couples to local phonon degrees of freedom. In the single site limit, at half-filling, the electron-phonon coupling results in a double well structure for the lattice displacement, favoring empty or doubly occupied sites. In two dimensions, and on a bipartite lattice in $d \geq 2$, an intersite hopping causes these doubly occupied and empty sites to alternate in a charge density wave (CDW) pattern when the temperature is lowered. Because a discrete symmetry is broken, this occurs in a conventional second-order transition at finite $T_{\rm cdw}$. In this paper, we investigate the effect of changing the phonon potential energy to one with an intrinsic double well structure even in the absence of an electron-phonon coupling. While this aids in the initial process of pair formation, the implications for subsequent CDW order are non-trivial. One expects that, when the electron-phonon coupling is too strong, the double wells become deep and the polaron mass large, an effect which reduces $T_{\rm cdw}$. We show here the existence of regions of parameter space where the double well potential, while aiding local pair formation, does so in a way which also substantially enhances long range CDW order.

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arXiv2022

A perspective on machine learning and data science for strongly correlated electron problems

Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times, challenges in recognizing novel phases, and the Fermion sign problem. Methods in machine learning (ML), artificial intelligence, and data science promise to help address these limitations and open up a new frontier in strongly correlated quantum system simulations. In this paper, we review some of the progress in this area. We begin by examining these approaches in the context of classical models, where their underpinnings and application can be easily illustrated and benchmarked. We then discuss cases where ML methods have enabled scientific discovery. Finally, we will examine their applications in accelerating model solutions in state-of-the-art quantum many-body methods like quantum Monte Carlo and discuss potential future research directions.

cond-mat.str-el↗

arXiv2021

Deconvolving the components of the sign problem

Auxiliary field Quantum Monte Carlo simulations of interacting fermions require sampling over a Hubbard-Stratonovich field $h$ introduced to decouple the interactions. The weight for a given configuration involves the products of the determinant of matrices $M_σ(h)$, where $σ$ labels the species, and hence is typically not positive definite. Indeed, the average sign $\langle {\cal S} \rangle$ of the determinants goes to zero exponentially with increasing spatial size and decreasing temperature for most Hamiltonians of interest. This statement, however, does not explicitly separate two possible origins for the vanishing of $\langle {\cal S} \rangle$. Does $\langle {\cal S} \rangle \rightarrow 0$ because {\it randomly} chosen field configurations have ${\rm det}\big(M(h)\big) < 0$, or does the `sign problem' arise because the specific subset of configurations chosen by the weighting function have a greater preponderance of negative values? In the latter case, the process of weighting the configurations with $|{\rm det}\big(M(h)\big)|$ might steer the simulation to a region of configuration space of $h$ where positive and negative determinants are equally likely, even though randomly chosen $h$ would preferentially have determinants with a single dominant sign. In this paper we address the relative importance of these two mechanisms for the vanishing of $\langle {\cal S} \rangle$ in quantum simulations.

cond-mat.str-el↗

arXiv2021

Quantum Monte Carlo study of an anharmonic Holstein model

We study the effects of anharmonicity on the physics of the Holstein model, which describes the coupling of itinerant fermions and localized quantum phonons, by introducing a quartic term in the phonon potential energy. We find that the presence of this anharmonic term reduces the extent of the charge density wave phase (CDW) at half-filling as well as the transition temperature to this phase. Doping away from half-filling, we observe a first order phase transition between the CDW and a homogeneous phase which is also present in the harmonic model. In addition, we study the evolution of the superconducting susceptibility in the doped region and show that anharmonicity can enhance the superconducting response.

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arXiv2020

Dynamical resilience to disorder: the dilute Hubbard model on the Lieb lattice

In itinerant systems, electron-electron interactions may lead to the formation of local magnetic moments and their effective exchange coupling, which in turn gives rise to long-range magnetic order. Therefore, when moment formation is weakened, such as in the single-band Hubbard model on a square lattice with the on-site repulsion being randomly switched off on a fraction $x$ of sites, magnetic order is suppressed beyond some critical $x_c$, which was found to lie below the classical percolation threshold, $x_c^\text{(perc,sq)}$. Here we study dilute magnetism in flat band systems, namely in the Hubbard model on a `Lieb' lattice. Interestingly, we show that magnetic order persists to $x$ almost twice as large as the classical percolation threshold for the lattice, thus emphasizing the central role of electron itinerancy to the magnetic response. The analysis of the orbital-resolved order parameters reveals that the contribution of the four-fold coordinated `d' sites to magnetism is dramatically affected by dilution, while the localized `p' states of the flat band provide the dominant contribution to long-range correlations. We also examine the transport properties, which suggest the existence of an insulator-to-metal transition in the same range of the critical magnetic dilution.

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arXiv2019

Competition between Phase Separation and Spin Density Wave or Charge Density Wave Order: Role of Long-Range Interactions

Recent studies of pairing and charge order in materials such as FeSe, SrTiO$_3$, and 2H-NbSe$_2$ have suggested that momentum dependence of the electron-phonon coupling plays an important role in their properties. Initial attempts to study Hamiltonians which either do not include or else truncate the range of Coulomb repulsion have noted that the resulting spatial non-locality of the electron-phonon interaction leads to a dominant tendency to phase separation. Here we present Quantum Monte Carlo results for such models in which we incorporate both on-site and intersite electron-electron interactions. We show that these can stabilize phases in which the density is homogeneous and determine the associated phase boundaries. As a consequence, the physics of momentum dependent electron-phonon coupling can be determined outside of the trivial phase separated regime.

cond-mat.str-el↗

arXiv2019

Effect of Strain on Charge Density Wave Order in the Holstein Model

We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-δ, 1 + δ$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that the CDW transition temperature is relatively insensitive to moderate anisotropy $δ\lesssim 0.3$, but begins to decrease more rapidly at $δ\gtrsim 0.4$. However, the density correlations, as well as the kinetic energies parallel and perpendicular to the compressional axis, change significantly for moderate $δ$. Accompanying mean-field theory calculations show a similar qualitative structure, with the transition temperature relatively constant at small $δ$ and a more rapid decrease for larger strains. We also obtain the density of states $N(ω)$, which provides clear signal of the charge ordering transition at large strain, where finite size scaling of the charge structure factor is extremely difficult because of the small value of the order parameter.

cond-mat.str-el↗

arXiv2019

Coherence Temperature in the Diluted Periodic Anderson Model

The Kondo and Periodic Anderson Model (PAM) are known to provide a microscopic picture of many of the fundamental properties of heavy fermion materials and, more generally, a variety of strong correlation phenomena in $4f$ and $5f$ systems. In this paper, we apply the Determinant Quantum Monte Carlo (DQMC) method to include disorder in the PAM, specifically the removal of a fraction $x$ of the localized orbitals. We determine the evolution of the coherence temperature $T^*$, where the local moments and conduction electrons become entwined in a heavy fermion fluid, with $x$ and with the hybridization $V$ between localized and conduction orbitals. We recover several of the principal observed trends in $T^*$ of doped heavy fermions, and also show that, within this theoretical framework, the calculated Nuclear Magnetic Resonance (NMR) relaxation rate tracks the experimentally measured behavior in pure and doped CeCoIn$_5$. Our results contribute to important issues in the interpretation of local probes of disordered, strongly correlated systems.

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arXiv2019

Charge Order in the Holstein Model on a Honeycomb Lattice

The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin liquid phase between the semi-metal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo (DQMC) to study the Holstein model on a Honeycomb lattice and explore the role of electron-phonon interactions on Dirac fermions. We show that they give rise to charge density wave (CDW) order, and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.

cond-mat.str-el↗

arXiv2019

One-dimensional Hubbard-Holstein model with finite range electron-phonon coupling

The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling $g$ to the phonons drives the system towards a Peierls charge density wave state whereas increasing the electron-electron interaction $U$ drives the fermions into a Mott antiferromagnet. At low $g$ and $U$, or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with characteristic range $ξ$, interpolating between the Holstein and Fröhlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $ξ$, and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction $U$ will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U \ne 0$ case, even for small values of the coupling range.

cond-mat.str-el↗

arXiv2019

Pressure Effects on the 4f Electronic Structure of Light Lanthanides

Using the satellite structure of the $L_{\gamma1}$ line in non-resonant x-ray emission spectra, we probe the high-pressure evolution of the bare 4f signature of the early light lanthanides at ambient temperature. For Ce and Pr the satellite peak experiences a sudden reduction concurrent with their respective volume collapse (VC) transitions. These new experimental results are supported by calculations using state-of-the-art extended atomic structure codes for Ce and Pr, and also for Nd, which does not exhibit a VC. Our work suggests that changes to the 4f occupation are more consistently associated with evolution of the satellite than is the reduction of the 4f moment. Indeed, we show that in the case of Ce, mixing of a higher atomic angular momentum state, driven by the increased hybridization, acts to obscure the expected satellite reduction. These measurements emphasize the importance of a unified study of a full set of microscopic observables to obtain the most discerning test of the underlying, fundamental f-electron phenomena at high pressures.

cond-mat.str-el↗

arXiv2017

Phonon dispersion and the competition between pairing and charge order

The Holstein Model (HM) describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits, but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature $T_{\rm cdw}$ for CDW order, and also uncover several novel features of diagonal long range order in the phase diagram, including a competition between charge patterns at momenta ${\bf q}=(π,π)$ and ${\bf q}=(0,π)$ which lends insight into the relationship between Fermi surface nesting and the wavevector at which charge order occurs. We also demonstrate SC order at half-filling in situations where nonzero bandwidth sufficiently suppresses $T_{\rm cdw}$.

cond-mat.str-el↗

arXiv2017

Compressible Ferrimagnetism in the depleted Periodic Anderson Model

Tight-binding Hamiltonians with single and multiple orbitals exhibit an intriguing array of magnetic phase transitions. In most cases the spin ordered phases are insulating, while the disordered phases may be either metallic or insulating. In this paper we report a Determinant Quantum Monte Carlo study of interacting electrons in a geometry which can be regarded as a two-dimensional Periodic Anderson Model with depleted interacting ($f$) orbitals. For a single depletion, we observe an enhancement of antiferromagnetic correlations and formation of localized states. For half of the $f$-orbitals regularly depleted, the system exhibits a ferrimagnetic ground state. We obtain a quantitative determination of the nature of magnetic order, which we discuss in the context of Tsunetsugu's theorem, and show that, although the dc conductivity indicates insulating behavior at half-filling, the compressibility remains finite.

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arXiv2017

Quantum phase transitions of multi-species Dirac fermions

We use the determinant Quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $π$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength $U_c$ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the band width. Although $U_c$ is monotonic, at fixed inverse temperature $β$ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be non-monotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.

cond-mat.str-el↗

arXiv2017

Tricriticality in Crossed Ising Chains

We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb$_{12}$O$_{29}$ and also, conceptually, as a geometry which is intermediate between one and two dimensions. Using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we present evidence that this model belongs to the 2D Ising universality class.

cond-mat.stat-mech↗

arXiv2016

Magnetic Order-Disorder Transitions on a 1/3 - Depleted Square Lattice

Quantum Monte Carlo simulations are used to study the magnetic and transport properties of the Hubbard Model, and its strong coupling Heisenberg limit, on a one-third depleted square lattice. This is the geometry occupied, after charge ordering, by the spin-$\frac{1}{2}$ Ni$^{1+}$ atoms in a single layer of the nickelate materials La$_4$Ni$_3$O$_8$ and (predicted) La$_3$Ni$_2$O$_6$. Our model is also a description of strained graphene, where a honeycomb lattice has bond strengths which are inequivalent. For the Heisenberg case, we determine the location of the quantum critical point (QCP) where there is an onset of long range antiferromagnetic order (LRAFO), and the magnitude of the order parameter, and then compare with results of spin wave theory. An ordered phase also exists when electrons are itinerant. In this case, the growth in the antiferromagnetic structure factor coincides with the transition from band insulator to metal in the absence of interactions.

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arXiv2016

Impurities near an Antiferromagnetic-Singlet Quantum Critical Point

Heavy fermion systems, and other strongly correlated electron materials, often exhibit a competition between antiferromagnetic (AF) and singlet ground states. Using exact Quantum Monte Carlo (QMC) simulations, we examine the effect of impurities in the vicinity of such AF- singlet quantum critical points, through an appropriately defined impurity susceptibility, $χ_{imp}$. Our key finding is a connection, within a single calculational framework, between AF domains induced on the singlet side of the transition, and the behavior of the nuclear magnetic resonance (NMR) relaxation rate $1/T_1$. We show that local NMR measurements provide a diagnostic for the location of the QCP which agrees remarkably well with the vanishing of the AF order parameter and large values of $χ_{imp}$. We connect our results with experiments on Cd-doped CeCoIn$_5$.

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