[Paper Review] Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study

Xue-Jia Yu, Zhiming Pan+2 more|arXiv (Cornell University)|Feb 20, 2023

Quantum Mechanics and Non-Hermitian Physics115 references4 citations

TL;DR

This study develops a sign-problem-free projector quantum Monte Carlo (QMC) method to investigate non-Hermitian strongly correlated Dirac fermions in the honeycomb Hubbard model. It reveals that non-Hermitian asymmetric hopping enhances antiferromagnetic order and that the quantum phase transition between Dirac semimetal and antiferromagnetic order belongs to the XY universality class, indicating emergent Hermiticity at the critical point.

ABSTRACT

Exotic quantum phases and phase transition in the strongly interacting Dirac systems has attracted tremendous interests. On the other hand, non-Hermitian physics, usually associated with dissipation arising from the coupling to environment, emerges as a frontier of modern physics in recent years. In this letter, we investigate the interplay between non-Hermitian physics and strong correlation in Dirac-fermion systems. We develop a sign-problem-free projector quantum Monte-Carlo (QMC) algorithm for the non-Hermitian interacting fermionic systems. Employing state-of-the-art projector QMC simulation, we decipher the ground-state phase diagram of the Honeycomb Hubbard model in the presence non-Hermitian asymmetric spin resolved hopping processes. Intriguingly, the antiferromagnetic ordering induced by Hubbard interaction is enhanced by the non-Hermitian asymmetric hopping. More remarkably, our study reveals that critical properties of the quantum phase transition between Dirac semi-metal and AF ordered phases are consistent with the XY universality class in Hermitian system, implying Hermiticity is emergent at the quantum critical point. The numerically-exact QMC approach utilized in this study is easily applied to other non-Hermitian interacting fermionic models, hence paving a new avenue to investigating quantum many-body physics in non-Hermitian systems.

Motivation & Objective

• To investigate the interplay between non-Hermitian physics and strong electron correlations in Dirac fermion systems.
• To develop a sign-problem-free quantum Monte Carlo algorithm for non-Hermitian interacting fermionic systems.
• To determine the ground-state phase diagram of the non-Hermitian honeycomb Hubbard model with asymmetric spin-resolved hopping.
• To examine the critical behavior of the quantum phase transition between Dirac semimetal and antiferromagnetic order.
• To assess whether non-Hermiticity alters critical universality or leads to emergent Hermitian behavior at quantum criticality.

Proposed method

• A sign-problem-free projector quantum Monte Carlo (QMC) algorithm is developed for non-Hermitian interacting fermionic systems, enabling numerically exact simulations.
• The method is applied to the honeycomb Hubbard model with non-Hermitian asymmetric spin-resolved hopping terms, modeled via complex hopping amplitudes.
• The ground-state phase diagram is mapped using large-scale QMC simulations with controlled statistical and finite-size extrapolations.
• Critical exponents and scaling behavior are extracted via finite-size scaling analysis to identify the universality class of the quantum phase transition.
• The non-Hermitian term is treated as a perturbation in the effective field theory, and one-loop renormalization group analysis is performed to study the relevance of non-Hermiticity at the critical point.
• The effective field theory includes a Yukawa coupling between Dirac fermions and a scalar field, with non-Hermitian terms introduced via a complex vector-like coupling.

Figure 1: Schematic asymmetry hopping (a) and ground state phase diagram (b) of non-Hermitian interacting model on the honeycomb lattice. In (a), the red(blue) circles represent the sites in A(B) sublattice. In (b), NHEAFM denotes non-Hermitian enhanced antiferromagnetism ordered phase and DSM denot

Experimental results

Research questions

• RQ1 How does non-Hermitian asymmetric hopping affect the stability of antiferromagnetic order in strongly correlated Dirac fermion systems?
• RQ2 What is the critical universality class of the quantum phase transition between the Dirac semimetal and antiferromagnetic phases in the presence of non-Hermiticity?
• RQ3 Is non-Hermiticity a relevant or irrelevant perturbation at the quantum critical point?
• RQ4 Can a sign-problem-free QMC method be constructed for non-Hermitian interacting fermionic systems?
• RQ5 Does the emergence of Hermitian criticality suggest a deeper symmetry restoration at the quantum critical point?

Key findings

• Non-Hermitian asymmetric hopping enhances antiferromagnetic ordering in the honeycomb Hubbard model, indicating a stabilization of long-range magnetic order.
• The quantum phase transition between the Dirac semimetal and antiferromagnetic Mott insulator phases belongs to the XY universality class, as confirmed by critical exponents and scaling collapse.
• The critical behavior remains consistent with the Hermitian Gross-Neveu-Yukawa-XY universality class, implying that Hermiticity is effectively restored at the quantum critical point.
• The non-Hermitian parameter δ is found to be an irrelevant perturbation at the quantum critical point, with its renormalization group flow driven to zero.
• The one-loop renormalization group analysis shows that δ flows as dδ/dl = -2ĝ²δ, confirming its irrelevance at the critical point.
• The developed QMC method is sign-problem-free and applicable to a broad class of non-Hermitian interacting fermionic models, enabling exact numerical studies of quantum many-body physics in such systems.

Figure 2: Finite-size scaling of XY-AFM static structure factor $S^{XY}_{AF}$ at different non-Hermitian parameter $\delta$ and Hubbard interaction $U$ close to the DSM-AFM transition. (a) $\delta=0.2$ , $U_{c}\approx 3.8$ . (b) $\delta=0.4$ , $U_{c}\lesssim 3.6$ . (c) $\delta=0.6$ , $U_{c}\lesssim