arXiv subjects

B. Sriram Shastry

Publications and source records attributed to B. Sriram Shastry.

At least 19 recordsLinked to original sources

arXiv2026

Weyl's Relations, Integrable Matrix Models and Quantum Computation

Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to this subspace. This setup is used to construct a hierarchy of parameter-dependent commuting matrices in $N$ dimensions. This family of commuting matrices is then related to Type-1 matrices representing quantum integrable models. The commuting matrices find an interesting application in quantum computation, specifically in Grover's database search problem. Each member of the hierarchy serves as a candidate Hamiltonian for quantum adiabatic evolution and, in some cases, achieves higher fidelity than standard choices -- thus offering improved performance.

quant-ph↗

arXiv2025

The $1/r^2$ Integrable system: The Universal Hamiltonian for Quantum Chaos

We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their eigenvalues under changes of parameters. The robustness of bulk space-time correlations of a many particle system to changing boundary conditions is suggested to be at the root of the universality. The explicit density-density correlation functions of the $1/r^2$ model, now available through the above mapping at two values of the coupling constant, are interpreted in the light of Bethe's {\it Ansatz}, giving a vivid picture of the fractionalization of bare particles or holes into ``quark'' like Bethe quasi-particles and holes.

cond-mat↗

arXiv2025

Super Lax Pairs and Infinite Symmetries in The $1/r^2$ System

We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2 $ family of interactions. The algebra consists of the commutation between a ``Super- Hamiltonian'', and two other operators, in a Hilbert space that is an enlargement of the original one by introducing fermions. The commutation relations reduce to quantal Ordered Lax equations when projected to the original subspace, and to a statement about the ``Harmonic Lattice Potential'' structure of the Lax operator. These in turn lead to a highly automatic proof of the integrability of these models. In the case of the discrete $SU(n)-1/r^2$ model, the `` Super-Hamiltonian'' is again an $SU(m)-1/r^2$ model with a related $m$, providing an interesting hierarchy of models.

cond-mat↗

arXiv2025

What Does The Korringa Ratio Measure?

We present an analysis of the Korringa ratio in a dirty metal, emphasizing the case where a Stoner enhancement of the uniform susceptibilty is present. We find that the relaxation rates are significantly enhanced by disorder, and that the inverse problem of determining the bare density of states from a study of the change of the Knight shift and relaxation rates with some parameter, such as pressure, has rather constrained solutions, with the disorder playing an important role. Some preliminary applications to the case of chemical substitution in the Rb$_{3-x}$K$_x $C$_{60}$ family of superconductors is presented and some other relevant systems are mentioned.

cond-mat↗

arXiv2024

Order by projection in single-band Hubbard model: a DMRG study

In a Fermi system near or at half-filling, a specific superconducting pairing channel, if not explicitly included in the Hamiltonian, can be boosted by suppressing a competing pairing channel; this is exemplified by the enhancement of extended $s$-wave correlations upon suppressing $s$-wave Cooper pairing. This phenomenon, originally found by the use of generalized uncertainty relations is referred to as \emph{order by projection}. The case of zero on-site Coulomb interaction in the thermodynamic limit, confirms this mechanism through the analytical solution. In this study, we go further and systematically investigate this mechanism for a strongly correlated fermionic Hubbard model, now with finite on-site interaction, on a square lattice with an extended set of hopping parameters. We explore the behaviors of different pairing channels when one of them is suppressed, utilizing density matrix renormalization group calculations. Our findings provide numerical evidence supporting the existence of \emph{order by projection} in the strongly correlated system we studied. We also investigate the effect of the strength of Hubbard $U$, next-nearest neighbor $t'$, hole-doping, as well as finite-size scaling approaching the thermodynamic limit.

cond-mat.str-el↗

arXiv2019

Quadratic to linear magnetoresistance tuning in TmB4

The change of a material's electrical resistance (R) in response to an external magnetic field (B) provides subtle information for the characterization of its electronic properties and has found applications in sensor and storage related technologies. In good metals, Boltzmann's theory predicts a quadratic growth in magnetoresistance (MR) at low B, and saturation at high fields. On the other hand, a number of nonmagnetic materials with weak electronic correlation and low carrier concentration for metallicity, such as inhomogeneous conductors, semimetals, narrow gap semiconductors and topological insulators, two-dimensional electron gas (2DEG) show positive, non-saturating linear magnetoresistance (LMR). However, observation of LMR in single crystals of a good metal is rare. Here we present low-temperature, angle dependent magnetotransport in single crystals of the antiferromagnetic metal, TmB4. We observe large, positive and anisotropic MR(B), which can be tuned from quadratic to linear by changing the direction of the applied field. In view of the fact that isotropic, single crystalline metals with large Fermi surface (FS) are not expected to exhibit LMR, we attribute our observations to the anisotropic FS topology of TmB4. Furthermore, the linear MR is found to be temperature-independent, suggestive of quantum mechanical origin.

cond-mat.str-el↗

arXiv2018

Extremely correlated fermi liquid of $t$-$J$ model in two dimensions

We study the two-dimensional $t$-$J$ model with second neighbor hopping parameter $t'$ and in a broad range of doping $δ$ using a closed set of equations from the {\em Extremely Correlated Fermi Liquid} (ECFL) theory. We obtain asymmetric energy distribution curves and symmetric momentum distribution curves of the spectral function, consistent with experimental data. We further explore the Fermi surface and local density of states for different parameter sets. Using the spectral function, we calculate the resistivity, Hall number and spin susceptibility. The curvature change in the resistivity curves with varying $δ$ is presented and connected to intensity loss in Angle Resolved Photoemission Spectroscopy (ARPES) experiments. We also discuss the role of the super-exchange $J$ in the spectral function and the resistivity in the optimal to overdoped density regimes.

cond-mat.str-el↗

arXiv2018

Reversal of particle-hole scattering-rate asymmetry in Anderson impurity model

We study the particle-hole asymmetry of the scattering rate in strongly correlated electron systems by examining the cubic $ω^3$ and $ωT^2$ terms in the imaginary part of the self-energy of the Anderson impurity model. We show that the sign is opposite in the weak-coupling and strong-coupling limits, explaining the differences found in theoretical approaches taking the respective limits as the starting points. The sign change in fact precisely delineates the cross-over between the weak and strong correlation regimes of the model. For weak interaction $U$ the sign reversal occurs for small values of the doping $δ=1-n$, while for interaction of order $U \approx 2 Γ$, $Γ$ being the hybridization strength, the cross-over curve rapidly shifts to the large-doping range. This curve based on the impurity dynamics is genuinely different from other cross-over curves defined through impurity thermodynamic and static properties.

cond-mat.str-el↗

arXiv2018

Nonresonant Raman Scattering in Extremely Correlated Fermi Liquids

We present theoretical results for the optical conductivity and the non-resonant Raman susceptibilities for three principal polarization geometries relevant to the square lattice. The susceptibilities are obtained using the recently developed extremely correlated Fermi liquid theory for the two-dimensional t-t'-J model, where t and t' are the nearest and second neighbor hopping. Our results are sensitively depending on t, t'. By studying this quartet of related dynamical susceptibilities, and their dependence on t, t', doping and temperature, we provide a useful framework for interpreting and planning future Raman experiments on the strongly correlated matter.

cond-mat.str-el↗

arXiv2018

The t-t'-J model in one dimension using extremely correlated Fermi liquid theory and time dependent density matrix renormalization group

We study the one dimensional t-t'-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.

cond-mat.str-el↗

arXiv2017

Extremely Correlated Fermi Liquid theory of the $t$-$J$ model in 2 dimensions: Low Energy properties

Low energy properties of the metallic state of the 2-dimensional tJ model are presented at various densities and temperatures for second neighbor hopping t', with signs that are negative or positive corresponding to hole or electron doping. The calculation employs a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations, when used in $d=\infty$ reproduce most of the known low energies features of the $U=\infty$ Hubbard model. In 2-dimensions we are able to study the variations due to the superexchange J. The resulting Dyson self energy is found to be momentum dependent as expected. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity and cotangent of the Hall angle in experimentally relevant units. These display significant thermal sensitivity for density n >~ 0.8, signifying an effective Fermi-liquid temperature scale which is two or three orders of magnitude below the bare bandwidth. Flipping the sign of the hopping t', i.e. studying hole versus electron doping, is found to induce a change in curvature of the temperature dependent resistivity from convex to concave at low temperatures. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.

cond-mat.str-el↗

arXiv2016

Integrable matrix theory: Level statistics

We study level statistics in ensembles of integrable $N\times N$ matrices linear in a real parameter $x$. The matrix $H(x)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i(x)$ (integrals of motion) $\left[H(x),H^i(x)\right] = 0$, $\left[H^i(x), H^j(x)\right]$ = 0, for all $x$. In a recent work, we developed a basis-independent construction of $H(x)$ for any $n$ from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the $N\to\infty$ limit provided $n$ scales at least as $\log{N}$; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values $x=x_0$ or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at $ \mathcal{O}(N^{-0.5})$ deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest neighbor level statistics.

cond-mat.mes-hall↗

arXiv2016

Rotationally invariant ensembles of integrable matrices

We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N-M independent commuting N-by-N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, in a manner similar to the construction of Gaussian ensembles in the RMT.

cond-mat.mes-hall↗

arXiv2016

Hysteretic magnetoresistance and unconventional anomalous Hall effect in the frustrated magnet TmB_4

We study TmB_4, a frustrated magnet on the Archimedean Shastry-Sutherland lattice, through magnetization and transport experiments. The lack of anisotropy in resistivity shows that TmB_4 is an electronically three-dimensional system. The magnetoresistance (MR) is hysteretic at low-temperature even though a corresponding hysteresis in magnetization is absent. The Hall resistivity shows unconventional anomalous Hall effect (AHE) and is linear above saturation despite a large MR. We propose that complex structures at magnetic domain walls may be responsible for the hysteretic MR and may also lead to the AHE.

cond-mat.str-el↗

arXiv2016

Removing the spin ice cap: magnetic ground states of rare earth tripod kagome lattice Mg$_2$RE$_3$Sb$_3$O$_{14}$ (RE = Gd, Dy, Er)

We present the structural and magnetic properties of a new compound family, Mg$_2$RE$_3$Sb$_3$O$_{14}$ (RE = Gd, Dy, Er), with a hitherto unstudied frustrating lattice, the "tripod kagome" structure. Susceptibility (ac, dc) and specific heat exhibit features that are understood within a simple Luttinger-Tisza type theory. For RE = Gd, we found long ranged order (LRO) at 1.65 K, which is consistent with a 120 $^{\circ}$ structure, demonstrating the importance of diople interactions for this 2D Heisenberg system. For RE = Dy, LRO at 0.37 K is related to the "kagome spin ice (KSI)" physics for a 2D system. This result shows that the tripod kagome structure accelerates the transition to LRO predicted for the related pyrochlore systems. For RE = Er, two transitions, at 80 mK and 2.1 K are observed, suggesting the importance of quantum fluctuations for this putative XY system.

cond-mat.str-el↗

arXiv2016

Renormalization Group Study of a Fragile Fermi liquid in $1+ε$ dimensions

We present a calculation of the low energy Greens function in $1+ε$ dimensions using the method of extended poor man's scaling, developed here. We compute the wave function renormalization $Z(ω)$ and also the decay rate near the Fermi energy. Despite the lack of $ω^2$ damping characteristic of 3-dimensional Fermi liquids, we show that quasiparticles do exist in $1+ε$ dimensions, in the sense that the quasiparticle weight $Z$ is finite and that the damping rate is smaller than the energy. We explicitly compute the crossover from this behavior to a 1-dimensional type Tomonaga-Luttinger liquid behavior at higher energies.

cond-mat.str-el↗

arXiv2016

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess "additional" integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

cond-mat.dis-nn↗

arXiv2015

Diagrammatic $λ$ series for extremely correlated Fermi liquids

The recently developed theory of extremely correlated Fermi liquids (ECFL), applicable to models involving the physics of Gutzwiller projected electrons, shows considerable promise in understanding the phenomena displayed by the $t$-$J$ model. Its formal equations for the Greens function are reformulated by a new procedure that is intuitively close to that used in the usual Feynman-Dyson theory. We provide a systematic procedure by which one can draw diagrams for the $λ$-expansion of the ECFL introduced in Ref. (9), where the parameter $λ\in (0,1)$ counts the order of the terms. In contrast to the Schwinger method originally used for this problem, we are able to write down the $n^{th}$ order diagrams ($O(λ^n)$) directly with the appropriate coefficients, without enumerating all the previous order terms. This is a considerable advantage since it thereby enables the possible implementation of Monte Carlo methods to evaluate the $λ$ series directly. The new procedure also provides a useful and intuitive alternative to the earlier methods.

cond-mat.str-el↗