arXiv subjects

Sudip Chakravarty

Publications and source records attributed to Sudip Chakravarty.

At least 19 recordsLinked to original sources

arXiv2023

A theorem of Kohn applied to quantum oscillations in Cuprates

In this note I apply a theorem of Kohn to quantum oscillations in cuprates. I show that when combined with Gell-Mann and Low theorem, there is rigorous justification of quantum oscillations as in a Fermi liquid for cuprates. The Gell-Man-Low theorem is not perturbative, and applies more generally as long as the adiabatic evolution from an isolated non-degenerate state is the case. Oscillation frequencies are identical to the non-interacting problem. Thus, quantum oscillations protect the Fermi liquid and is in turn protected by it. This is not to imply that other properties of the cuprates that do not have a gap in the spectrum could not exhibit non-Fermi liquid behavior, for example, angle resolved photoemission spectroscopy.

cond-mat.supr-con↗

arXiv2023

Planckian dissipation and $c$-axis superfluid density in cuprate superconductors

An interesting concept in condensed matter physics is Planckian dissipation, in particular its manifestation in a remarkable phenomenology of superfluid density as a function of superconducting transition temperature. The concept was ontroduced for $ab$-plane properties. However, when suitably interpreted, it can also be applicable to the incoherent $c$-axis resistivity, which has not been adequately addressed previously. There are two results in this note: the first is a derivation using Kubo formula as to how Planckian dissipation could arise. It is aided by the fact that the $c$-axis tunneling matrix element is so small that a second order perturbation theory combined with presumed non-Fermi liquid behavior is sufficient to illuminate the phenomonon. In addition, the notion of quantum criticality plays an important role.

cond-mat.supr-con↗

arXiv2023

Quantum critical fans from critical lines at zero temperature

Quantum critical phenomena influences the finite temperature behavior of condensed matter systems through quantum critical fans whose extents are determined by the exponents of the zero temperature criticality. Here we emphasize the aspects of quantum critical lines, as discussed previously, and study an exactly solved model involving a transverse field Ising model with added three-spin interaction. This model has three critical lines. We compute the spin-spin correlation function and extract the correlation length, and identify the crossovers: quantum critical to quantum disordered, or renormalized classical regimes. We construct the quantum critical fans along one of the critical lines. In addition, we also construct finite temperature dynamic structure factors. We hope this model will become experimentally realizable in the future, and our results could stimulate studies in many similar models.

cond-mat.str-el↗

arXiv2022

Quantum critical points, lines and surfaces

In this paper we promote the idea of quantum critical lines ({\em inter alia} surfaces) as opposed to points. A quantum critical line obtains when criticality at zero temperature is extended over a continuum in a one-dimensional line. We base our ideas on a simple but exactly solved model introduced by one of the authors involving a one-dimensional quantum transverse field Ising model with added 3-spin interaction. While many of the ideas are quite general, there are other aspects that are not. In particular, a line of criticality with continuously varying exponents is not captured. However, the exact solvability of the model gives us considerable confidence in our results. Although the pure system is analytically exactly solved, the disorder case requires numerical analyses based on exact computation of the correlation function in the Pfaffian representation. The disorder case leads to dynamic structure factor as a function of frequency and wave vector. We expect that the model is experientally realizable and perhaps many other similar models will be found to explore quantum critical lines.

cond-mat.str-el↗

arXiv2020

Density Wave Mediated Dzyaloshinskii-Moriya Interactions

We investigate the effect that density wave states have on the localized spins of a square lattice. We find that topologically nontrivial density wave states can induce stable Dzyaloshinskii-Moriya (DM) interactions among the localized spins of the lattice in the presence of an external magnetic field, and we study the resulting spin models for both antiferromagnetic and ferromagnetic backgrounds. While the density wave state itself can contribute to the the thermal Hall effect, as shown by Li & Lee (arXiv:1905.04248v3), symmetry considerations preclude the resulting spin excitations from inducing a further thermal Hall effect. We utilize a Holstein-Primakoff (HP) substitution about the classical mean-field ground state to calculate the magnon dispersion for LSCO and find that the density wave induces a weak $d_{x^2-y^2}$ anisotropy; upon calculating the non-Abelian Berry curvature for this magnon branch we show explicitly that the magnon contribution to $κ_{xy}$ is zero. Finally, we calculate corrections to the magnetic ground state energy, spin canting angles, and the spin-wave dispersion due to the topological density wave for ferromagnetic backgrounds. We find that terms linear in the HP bosons can affect the critical behavior, a point previously overlooked in the literature.

cond-mat.str-el↗

arXiv2020

Quantum critical fluctuations, Planckian dissipation, and compactification scale

The most striking result here is that the notion of Planckian dissipation is also applicable to the $c$-axis resistivity of the high temperature cuprate superconductors, and to my knowledge this aspect has not been previously addressed. The derivation involves Kubo formula and does not require any mechanism beyond a non-Fermi liquid assumption. The $c$-axis resistivity, in its essential aspects, is discussed in the context of quantum critical point. Finally, I consider a zero temperature problem with one of its spatial dimensions compactified. The warning is that this compatification scale at the quantum critical point behaves similarly to the finite temperature problem, but obviously being at zero temperature there is no dissipation.

cond-mat.str-el↗

arXiv2019

Unsupervised Learning Eigenstate Phases of Matter

Supervised Learning has been successfully used to produce phase diagrams and identify phase boundaries when local order parameters are unavailable. Here, we apply unsupervised learning to this task. By using readily available clustering algorithms, we are able to extract the distinct eigenstate phases of matter within the transverse-field Ising model in the presence of interactions and disorder. We compare our results to those found through supervised learning and observe remarkable agreement. However, as opposed to the supervised procedure, our method requires no strict assumptions concerning the number of phases present, no labeled training data, and no prior knowledge of the phase diagram. We conclude with a discussion of clustering and its limits.

cond-mat.str-el↗

arXiv2019

Spectra of the Dissipative Spin Chain

This paper generalizes the (0+1)-dimensional spin-boson problem to the corresponding (1+1)-dimensional version. Monte Carlo simulation is used to find the phase diagram and imaginary time correlation function. The real frequency spectrum is recovered by the newly developed Páde regression analytic continuation method. We find that, as dissipation strength $α$ is increased, the sharp quasi-particle spectrum is broadened and the peak frequency is lower. According to the behavior of the low frequency spectrum, we classify the dynamical phase into three different regions: weakly damped, linear $k$-edge, and strongly damped.

cond-mat.str-el↗

arXiv2018

Rational function regression method for numerical analytic continuation

A simple method for numerical analytic continuation is developed. It is designed to analytically continue the imaginary time (Matsubara frequency) quantum Monte Carlo simulation results to the real time (real frequency) domain. Such a method is based on the Padé approximation. We modify it to be a linear regression problem, and then use bootstrapping statistics to get the averaged result and estimate the error. Unlike maximum entropy method, no prior information is needed. Test-cases have shown that the spectrum is recovered for inputs with relative error as high as 1%.

physics.comp-ph↗

arXiv2018

Density Wave States in the Presence of an External Magnetic Field

We investigate the effect that density-wave states have on the Hofstadter Butterfly. We first review the problem of the $d$-density wave on a square lattice and then numerically solve the $d$-density wave problem when an external magnetic field is introduced. As the $d$-density wave condensation strength is tuned the spectrum evolves through three topologically distinct butterflies, and an unusual quantum Hall effect is observed. The chiral $p+ip$-density wave state demonstrates drastically different Hofstadter physics--inducing a destruction of the gaps in the butterfly which causes electrons' cyclotron orbits to not obey any type of Landau quantization, and the creation of a large gap in the spectrum with Hall conductance $σ_{xy}$=0. To investigate the quantum phases in the system we perform a multifractal analysis of the single particle wavefunctions. We find that tuning the $d$-density wave strength at a generic value of magnetic flux controls a metal-metal transition at charge neutrality where the wavefunction multifractality occurs near band touching events. In the $p+ip$ case we observe another metal-metal transition near a band touching event which is seperated by a quasi-insulating island state occuring at charge neutrality near strip dimerization of the lattice.

cond-mat.stat-mech↗

arXiv2018

Binary disorder in quantum Ising chains and induced Majorana zero modes

Dynamical structure factor (S(k,$ω$)) is calculated for the one-dimensional (1D) transverse field Ising model, and its recent extension to include a three spin term, with quenched binary disorder. We study the low energy modes for lattices as large as 256 sites. We show that the intense zero energy modes appear whenever the binary disorder straddles two different winding numbers. We argue that these are Majorana modes, which reside on the boundaries of the rare regions. The size distribution of Majorana pairs has a fractal behavior at the critical points. With the longer ranged interactions a spin glass transition is observed as well.

cond-mat.dis-nn↗

arXiv2018

Specific heat and pairing of Dirac composite fermions in the half-filled Landau level

A recent proposal argues that an alternate description of the half-filled Landau level is a theory of massless Dirac fermions. We examine the possibility of pairing of these Dirac fermions by numerically solving the {\em coupled} Eliashberg equations unlike our previous calculation [Wang and Chakravarty, Phys. Rev. B {\bf 94}, 165138 (2016)]. In addition, vertex corrections are calculated to be zero from the Ward identity. We find that pairing is possible in non-zero angular momentum channels; the only differences are minor numerical shifts. As before, the pairing leads to the gapped Pfaffian and anti-Pfaffian states. However, in our approximation scheme, pairing is not possible in the putative particle-hole symmetric state for $\ell=0$ angular momentum. The specific heat at low temperatures of a system of massless Dirac fermions interacting with a transverse gauge field, expected to be relevant for the half-filled Landau level, is calculated. Using the Luttinger formula, it is found be $\propto T\ln T$ in the leading low temperature limit, due to the exchange of transverse gauge bosons. The result agrees with the corresponding one in the nonrelativistic composite fermion theory of Halperin, Lee and Read of the half-filled Landau level.

cond-mat.str-el↗

arXiv2017

Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions

The quantum phase transition between two clean, non interacting topologically distinct gapped states in three dimensions is governed by a massless Dirac fermion fixed point, irrespective of the underlying symmetry class, and this constitutes a remarkably simple example of superuniversality. For a sufficiently weak disorder strength, we show that the massless Dirac fixed point is at the heart of the robustness of superuniversality. We establish this by considering both perturbative and nonperturbative effects of disorder. The superuniversality breaks down at a critical strength of disorder, beyond which the topologically distinct localized phases become separated by a delocalized diffusive phase. In the global phase diagram, the disorder controlled fixed point where superuniversality is lost, serves as a multicritical point, where the delocalized diffusive and two topologically distinct localized phases meet and the nature of the localization-delocalization transition depends on the underlying symmetry class. Based on these features we construct the global phase diagrams of noninteracting, dirty topological systems in three dimensions. We also establish a similar structure of the phase diagram and the superuniversality for weak disorder in higher spatial dimensions. By noting that $1/r^2$ power-law correlated disorder acts as a marginal perturbation for massless Dirac fermion in any spatial dimension $d$, we have established a general renormalization group framework for addressing disorder driven critical phenomena for fixed spatial dimension $d > 2$.

cond-mat.dis-nn↗

arXiv2016

Comment on "Magnetotransport signatures of a single nodal electron pocket constructed from Fermi arcs"

We comment on the recent work [N. Harrison, \textit{et al.} Phys. Rev. B {\bf 92}, 224505 (2015)] which attempts to explain the sign reversal and quantum oscillations of the Hall coefficient observed in cuprates from a single nodal diamond-shaped electron pocket with concave arc segments. Given the importance of this work, it calls for a closer scrutiny. Their conclusion of sign reversal of the Hall coefficient depends on a non-generic rounding of the sharp vertices. Moreover, their demonstration of quantum oscillation in the Hall coefficient from a single pocket is unconvincing. We maintain that at least two pockets with different scattering rates is necessary to explain the observed quantum oscillations of the Hall coefficient.

cond-mat.supr-con↗

arXiv2016

Can a quantum critical state represent a blackbody?

The blackbody theory of Planck played a seminal role in the development of quantum theory at the turn of the past century. A blackbody cavity is generally thought to be a collection of photons in thermal equilibrium; the radiation emitted is at all wavelengths, and the intensity follows a scaling law, which is Planck's characteristic distribution law. These photons arise from non-interacting normal modes. Here we suggest that certain quantum critical states when heated emit "radiation" at all wavelengths and satisfy all the criteria of a blackbody. An important difference is that the "radiation" does not necessarily consist of non-interacting photons, but also emergent relativistic bosons or fermions. The examples we provide include emergent relativistic fermions at a topological quantum critical point. This perspective on a quantum critical state may be illuminating in many unforeseen ways.

cond-mat.str-el↗

arXiv2016

Pairing of particle-hole symmetric composite fermions in half-filled Landau level

In a recent proposal of the half-filled Landau level, the composite fermions are taken to be Dirac particles and particle-hole symmetric. Cooper pairing of these composite fermions in different angular momentum channels, $\ell$, can give rise to different kinds of Pfaffian states. In addition to the well known Moore-Read Pfaffian and anti-Pfaffian states, a new putative particle-hole symmetric Pfaffian state, corresponding to the $s-$wave pairing channel, was also proposed. However, the possible underlying pairing mechanism is not clear at all. In this work we provide a specific pairing mechanism for realizing some of these Pfaffian states. We show that there can be nonzero pairing in angular momentum channels $|\ell|\ge 1$ depending on the magnitude of a coupling constant. There is a quantum phase transition from the Dirac composite fermi liquid state to Cooper pairing states in angular momentum channels $|\ell|\ge 1$ as the coupling constant is tuned across its critical point value. Surprisingly the particle-hole symmetric $\ell=0$ channel pairing turns out to be impossible irrespective of the size of the coupling constant.

cond-mat.str-el↗

arXiv2016

A calculation for polar Kerr effect in high temperature cuprate superconductors

A mechanism is proposed for the tantalizing evidence of polar Kerr effect in a class of high temperature superconductors--the signs of the Kerr angle from two opposite faces of the same sample are identical and magnetic field training is non-existent. The mechanism does not break global time reversal symmetry, as in an antiferromagnet, and results in zero Faraday effect. It is best understood in a phenomenological model of bilayer cuprates, such as YBCO, in which intra-bilayer tunneling nucleates a chiral d-density wave such that the individual layers have opposite chirality. Although specific to the chiral d-density wave, the mechanism may be more general to any quasi-two-dimensional orbital antiferromagnet in which time reversal symmetry is broken in each plane, but not when averaged macroscopically.

cond-mat.str-el↗

arXiv2016

Activated scaling in disorder rounded first-order quantum phase transitions

First-order phase transitions, classical or quantum, subject to randomness coupled to energy-like variables (bond randomness) can be rounded, resulting in continuous transitions (emergent criticality). We study perhaps the simplest such model, quantum three-color Ashkin-Teller model and show that the quantum critical point in $(1+1)$ dimension is an unusual one, with activated scaling at the critical point and Griffiths-McCoy phase away from it. The behavior is similar to the transverse random field Ising model, even though the pure system has a first-order transition in this case. We believe that this fact must be attended to when discussing quantum critical points in numerous physical systems, which may be first-order transitions in disguise.

cond-mat.dis-nn↗