arXiv subjects

Vibhu Mishra

Publications and source records attributed to Vibhu Mishra.

4 recordsLinked to original sources

arXiv2026

Umklapp correction to Landau damping and conditions for non-trivial modifications to quantum critical transport

We compute the particle--hole bubble for an Ising-nematic metal when the critical Fermi surface approaches the Brillouin zone boundary for $d=2$ dimensions. We find two qualitatively distinct contributions: i)~the standard antipodal piece, which gives $Π_{\rm{ATP}}(\mathbf{q}, iΩ)\proptoΩ/q$ and ii)~an additional umklapp piece from electrons near the zone boundary, which gives $Π_{\rm{U}}(\mathbf{q}, iΩ)\propto Ω^α$ at the minimum umklapp momentum $q\approx Δ_q$ with $α= 2/3 $ or $1/2$ depending on the temperature $T$. At high $T$ when $α= 1/2$, the minimum $T$ for the activation of linear/quasi-linear in $T$ resistivity, which is expected to be $T_U \propto Δ_q^3$ from $z=3$ criticality, could potentially get reduced to $T_U \propto Δ_q^4$ due to the $\sqrtΩ$ term and discuss why we find only one hyper-specific scenario where this possibility might be realized. For $d=3$ the umklapp contribution gives $Π_{\rm{U}}\sim Ω$ irrespective of $T$ therefore $T_U$ is not modified in this case.

cond-mat.str-el↗

arXiv2026

Marginal Fermi liquids from Fermi surfaces coupled via matrix boson gas

We propose a model of metallic critical point which we study at $T=0$ in the large-$N$ limit. We start with two species of fermions $u_i, d_i$, each with $N$ flavors and a gas of matrix bosons $b_{ij}$ with $N^2$ components. The fermions interact with each other via the intermediate boson as $\int b_{ij}^{\dagger} \, u_i^{\dagger}d_j$. The bosons have a bare dispersion $\varepsilon_{\textbf{q}}^b = λ_z |\textbf{q}|^z$ and we study the problem in $d$ spatial dimensions. We show that for $d = z+1,$ the electronic self energy shows marginal Fermi liquid behavior. We first evaluate the fermionic self energy $Σ(iω)$ using the standard approximate boson self energy $Π(\textbf{q}, iν) \propto |ν|/|\textbf{q}|$ and find that $Σ(iω) \sim ω\ln(N/|ω|)$ which shows a much weaker dependence on $N$ when compared with similar results from non-SYK large-$N$ Ising-nematic models. Then we evaluate $Σ(iω)$ again using a more precise form of $Π(\textbf{q}, iν)$ which allows us to study the interplay between $N \rightarrow \infty$ limit for which $Σ(iω) \sim ω\ln(1/|ω|)$, and the $ω\rightarrow 0$ limit where we recover $Σ(iω) \sim ω\ln(N/|ω|)$. We also use the full bosonic self energy to obtain the correction to the bosonic specific heat as $\frac{T}{N} \ln(1/T)$. Since there are $N^2$ bosons and $N$ fermions, the bulk heat capacity for both fermions and bosons shows nearly identical functional form $NVT \ln(N/T)$ and $NVT \ln(1/T)$ respectively for $T \rightarrow 0$. This suggests that coupling the hybridization operator $u^{\dagger}d$ to non-relativistic bosons for $d=3$ and relativistic bosons for $d=2$ provides a simple route to marginal Fermi liquid scaling.

cond-mat.str-el↗

arXiv2025

Rate Function Modelling of Quantum Many-Body Adiabaticity

The quantum adiabatic theorem is a fundamental result in quantum mechanics, with a multitude of applications, both theoretical and practical. Here, we investigate the dynamics of adiabatic processes for quantum many-body systems %in detail by analysing the properties of observable-free, intensive quantities. In particular, we study the adiabatic rate function $f(T, Δλ)$ in dependence of the ramp time $T$, which gives us a complete characterization of the many-body adiabatic fidelity as a function of $T$ and the strength of the parameter displacement $Δλ$. $f(T, Δλ)$ quantifies the deviation from adiabaticity for a given process and therefore allows us to control and define the notion of adiabaticity in many-body systems. First we study $f(T, Δλ)$ for the 1D transverse field Ising model and the Luttinger liquid, both of which are quadratic systems and therefore allow us to look at the thermodynamic limit. For ramps across gapped phases, we relate $f(T, Δλ)$ to the transition probability of the system and for ramps across a gapless point, or gapless phase we relate it to the excitation density of the relevant quasiparticles. Then we investigate the XXZ model which allows us to see the qualitative features that survive when interactions are turned on. Several key results in the literature regarding the interplay of the thermodynamic and the adiabatic limit are obtained as inferences from the properties of $f(T, Δλ)$ in the large $T$ limit.

quant-ph↗

arXiv2024

Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches

Charge-density wave phases in quantum materials stem from the complex interplay of electronic and lattice degrees of freedom. Nowadays, various time-resolved spectroscopy techniques allow to actively manipulate such phases and monitor their dynamics in real time. Modeling such nonequilibrium dynamics theoretically is a great challenge and exact methods can usually only treat a small number of atoms and finitely many phonons. We approach the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping from two perspectives: We prove that in the non-interacting and in the strong-coupling limit, the CDW order parameter on high-dimensional hypercubic lattices obeys a factorization relation for long times, such that its dynamics can be reduced to the one-dimensional case. Secondly, we present numerical results from semiclassical techniques based on the Truncated Wigner Approximation for two spatial dimensions. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics. This is confirmed, in addition, for a quench in the electron-phonon coupling strength.

cond-mat.str-el↗