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arXiv:2411.13273 · Physical Review Letters

Quantum Monte Carlo Study of Hydrodynamics in Systems with Particle-Hole Symmetry

Adrien Reingruber, Kitinan Pongsangangan, Fakher F. Assaad, Maksim Ulybyshev

Published May 23, 2025• 3 citations
arXivHTMLPDF

Abstract

The emergence of hydrodynamic behavior in electronic flow within clean, particle-hole-symmetric systems at half filling is a nontrivial problem. Navier-Stokes (NS) equations describe the momentum flow, while experimental measurements typically capture the current flow profiles. However, in particle-hole-symmetric systems, electric current and momentum flow are entirely decoupled, because electrons and holes move in opposite directions with equal distribution functions. This makes it challenging to link NS equations to observed flow patterns. In this Letter, we demonstrate that the hydrodynamic behavior of the charge current at half filling can emerge despite the absence of momentum flow. By combining Boltzmann transport theory with numerically exact quantum Monte Carlo simulations of clean graphene samples, we show that NS-type equations can be derived directly for the charge current, eliminating the need for any additional mechanism coupling the velocity field and charge current in explaining the experimentally observed hydrodynamic flow profiles in graphene at half filling. We show that a new transport quantity-the current diffusion coefficient-replaces viscosity and expect this description to be valid for any particle-hole-symmetric system. Our results provide new insights into the interpretation of experimental data and demonstrate how quantum Monte Carlo calculations can serve as an alternative to experiments in transport measurements to verify the kinetic theory results.

DOI
10.1103/physrevlett.134.206303

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The emergence of hydrodynamic behavior in electronic flow within clean, particle-hole-symmetric systems at half filling is a nontrivial problem. Navier-Stokes (NS) equations describe the momentum flow, while experimental measurements typically capture the current flow profiles. However, in particle-hole-symmetric systems, electric current and momentum flow are entirely decoupled, because electrons and holes move in opposite directions with equal distribution functions. This makes it challenging to link NS equations to observed flow patterns. In this Letter, we demonstrate that the hydrodynamic behavior of the charge current at half filling can emerge despite the absence of momentum flow. By combining Boltzmann transport theory with numerically exact quantum Monte Carlo simulations of clean graphene samples, we show that NS-type equations can be derived directly for the charge current, eliminating the need for any additional mechanism coupling the velocity field and charge current in explaining the experimentally observed hydrodynamic flow profiles in graphene at half filling. We show that a new transport quantity-the current diffusion coefficient-replaces viscosity and expect this description to be valid for any particle-hole-symmetric system. Our results provide new insights into the interpretation of experimental data and demonstrate how quantum Monte Carlo calculations can serve as an alternative to experiments in transport measurements to verify the kinetic theory results.
Abstract The superflow of water at nanoscale remains an open problem. Classical hydrodynamics predicts flow rates that are 2 to 5 orders of magnitude lower than those observed experimentally. Therefore, it is natural to question the validity of such models while exploring alternative approaches. In this work, we investigate the behavior of viscoplastic fluids, particularly Bingham fluids, from the perspective of de Broglie–Bohm quantum mechanics, incorporating the effects of a quantum potential (quantum hydrodynamics). We phenomenologically assume that the physics behind these unexplained experimental results might be associated to an effective quantum potential which properties that can be associated to an effective anti-dissipative hydrodynamical term in the classical approach. We combine a theoretical approach with its numerical solutions to understand the interplay between the Navier–Stokes-Bingham hydrodynamical system and the quantum hydrodynamics. Our results indicate that the quantum potential can be directly associated with the increased flow velocity, reinforcing that quantum effects may play a significant role in the dynamics of fluids confined within nanotubes. Moreover, well-behaved solutions for the system’s wavefunction were identified even in the exotic case of anti-dissipative fluid flow. This evidence provides a possible theoretical explanation for the superflux phenomenon, reinforcing the hypothesis that quantum effects may underlie the discrepancies relative to classical hydrodynamic predictions.
This thesis focuses on several examples of strongly correlated electronic quantum fluids. In chapter 2 we use a kinetic theory approach to describe the transport properties of bilayer graphene near charge neutrality. After solving the semiclassical Boltzmann equation, we find that the results are well approximated by a hydrodynamic two-fluid model. A fluid of electrons and a fluid of holes interact with each other via Coulomb drag. Chapter 3 looks at quantum Hall edges. We consider a quantum Hall edge coupled to a driven quantum dot and compute the current on the edge downstream from the contact. We show that Coulomb interactions between the dot and the edge renormalize the charge in the current pulses. Chapter 4 focuses on the bilayer quantum Hall system. Two layers of quantum Hall fluid are separated by a variable distance. At large interlayer separation, we have two well-separated composite Fermi liquids and we consider the pairing between the two layers as the interlayer separation is decreased. We propose a new trial state for this paired phase of matter and use exact diagonalization numerics to investigate this proposal.
We determine the information scrambling rate ${\ensuremath{\lambda}}_{L}$ due to electron-electron Coulomb interaction in graphene. ${\ensuremath{\lambda}}_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that ${\ensuremath{\lambda}}_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single-particle relaxation. Furthermore, ${\ensuremath{\lambda}}_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the timescale for these processes. In addition, we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.
We consider a hydrodynamic description of transport for generic two-dimensional electron systems that lack Galilean invariance and do not fall into the category of Fermi liquids. We study magnetoresistance and show that it is governed only by the electronic viscosity provided that the wavelength of the underlying disorder potential is large compared to the microscopic equilibration length. We also derive the Coulomb drag transresistance for double-layer non-Fermi-liquid systems in the hydrodynamic regime. As an example, we consider frictional drag between two quantum Hall states with half-filled lowest Landau levels, each described by a Fermi surface of composite fermions coupled to a U(1)U(1)U(1) gauge field. We contrast our results to prior calculations of drag of Chern-Simons composite particles and place our findings in the context of available experimental data.
The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the microscopic dynamics of nearly integrable 1D quantum many-body systems. We build upon the recently developed hydrodynamics of integrable models to study the effective Boltzmann equation with collision integral taking into account the non-integrable interactions. We compute the transport coefficients and find that the resulting Navier-Stokes equations have two regimes, which differ in the viscous properties of the fluid. We illustrate the method by computing the transport coefficients for an experimentally relevant case of coupled 1D cold-atomic gases.
Relativistic hydrodynamics is a low-energy e↵ective theory which universally describes macroscopic behaviors of relativistic many-body systems.Its application covers the broad branches of physics such as high-energy physics, astrophysics, and condensed matter physics.Nevertheless, its derivation from underlying microscopic theories, especially from quantum field theories, has not been clearly clarified.Furthermore, it is recently pointed out that novel transport phenomena such as the chiral magnetic e↵ect, which originates from the quantum anomaly in the underlying quantum field theories, take place in the macroscopic hydrodynamic regime.In this thesis, we derive relativistic hydrodynamics from quantum field theories on the basis of the recent development of nonequilibrium statistical mechanics.In order to derive the hydrodynamic equations we introduce an assumption that the density operator is given by a local Gibbs distribution at initial time, and decompose the energy-momentum tensor and charge current into nondissipative and dissipative parts.This leads to a generalization of the Gibbs ensemble method canonically employed in equilibrium statistical mechanics.Our formalism is also applicable to the situation in the presence of the quantum anomaly, and we can describe the anomaly-induced tranport phenomena.As a basic tool of our formalism, we first develop a path integral of the thermodynamic potential for locally thermalized systems.We show microscopically that the thermodynamic pontential, which is shown to be the generating functional of systems in local thermal equilibrium, is written in terms of the quantum field theory in the curved spacetime with one imaginary-time direction.The structure of this thermally emergent curved spacetime is determined by hydrodynamic variables such as the local temperature, and fluid-four velocity, and possesses notable symmetry properties: Kaluza-Klein gauge symmetry, spatial di↵eomorphism symmetry, and gauge symmetry.With the help of the symmetry argument, we can construct the nondissipative part of the hydrodynamic equations including the anomaly-induced transport phenomena.By the use of the perturbative calculation, we evaluate the anomalous transport coe cients at one-loop level.Furthermore, we also construct a solid basis to study dissipative corrections to hydrodynamic equations.In particular, by performing the derivative expansion, together with the result on nondissipative part of the constitutive relations, we derive the firstorder dissipative hydrodynamic equations, that is, the relativistic Navier-Stokes equation.Our formalism also provides the quantum field theoretical expression of the Green-Kubo formulas for transport coe cients.iii The formulation and whole works presented from Chapter 2 to Chapter 4 are based on our original work in collaboration with Yoshimasa Hidaka (RIKEN).The work presented in Chapter 3 is in collaboration with Yoshimasa Hidaka (RIKEN), Tomoya Hayata (RIKEN), and Toshifumi Noumi (Hong Kong University of Science and Technology) [1].1 There is close investigation of priority to the Navier-Stokes equation in Ref. [11].