Resolving Microscopic Correlated Electron Dynamics via 2000-Qubit Quantum Simulation

TL;DR

This work addresses how domain-wall networks in the strongly correlated material 1T-TaS2 relax after excitation, focusing on whether relaxation is driven by coherent multi-particle tunnelling or cascaded local events. The authors derive a low-energy TFIM description from a microscopic electron model and perform large-scale quantum simulations on a D-Wave device, revealing that domain-wall motion arises from second-order single-particle tunnelling enabled by a noisy, quasi-static environment. A scaling collapse shows the reconfiguration rate is weakly dependent on the intrinsic tunnelling amplitude, supporting a noise-assisted mechanism rather than tunnelling-limited dynamics. Overall, the study demonstrates that quantum simulation can function as a practical microscope to resolve non-equilibrium relaxation pathways in complex quantum materials and outlines a path to extend such analyses to more detailed models and experimental probes.

Abstract

Understanding how quantum materials return to equilibrium after being driven into excited states is a fundamental problem in condensed matter physics. A prototypical material, 1T-TaS$_2$, exhibits complex electronic textures made up of domain walls, which slowly reorganize into a more uniform structure as the system relaxes. At low temperatures, this process becomes dominated by quantum rather than thermal effects. In this work, we use large-scale noise-driven quantum simulations-spanning more than 2000 qubits-to study this relaxation process through an effective model known as the transverse-field Ising model in a longitudinal field. By mathematically transforming this model into a simpler form, we identify the basic microscopic steps involved: rather than moving collectively, the domain walls evolve through a sequence of noise-driven single-particle tunneling events. A detailed analysis of how the relaxation rate depends on temperature and model parameters confirms this picture. Our findings show that quantum simulation can provide rare, predictive insight into the inner workings of real quantum materials, and establish a practical pathway for studying complex non-equilibrium processes using current-generation quantum hardware.

Figures (4)

• Figure 1: Domain structures and relaxation in 1T-TaS$_2$ and in quantum simulation. (a) Representative CDW domain configuration in 1T-TaS$_2$, where colors denote the thirteen distinct commensurate CDW domains related by relative translations of the $1/13$-filled polaronic superlattice. Extended domain walls separate regions of different CDW domains and store excess interaction energy. (b) Corresponding domain configuration obtained in the quantum simulation on a quantum annealer. Colors label the three degenerate domains of the effective triangular-lattice transverse-field Ising model. Despite the reduced number of domain types, the local domain-wall geometry is the same as in the material. Black outlines and lines show (a) and (b) as insets of (c) and (d). (c) Time-resolved STM images of 1T-TaS$_2$ showing slow relaxation of an initially non-equilibrium domain-wall network toward the ordered ground state. (d) Representative sequence of configurations from the quantum simulation obtained via iterative annealing cycles, showing domain-wall annihilation and coarsening. (e) Evolution of polaron density and interaction energy extracted from STM measurements during relaxation in 1T-TaS$_2$, where domains are typically offset closer together due to an excess of charge and gradually reconfigure into a single domain through charge leakage. (f) Evolution of polaron density and interaction energy obtained from the quantum simulation. The system initializes with missing charge, evidenced by a typical neighboring domain offset moving them away from each other, and leading to an increase in polaron number during relaxation. Despite this global difference, the local polaronic dynamics within domain walls are the same in experiment and simulation, as shown in this work.
• Figure 2: (a) Four representative configurations involved in domain wall dynamics in the TFIM. In the effective Hamiltonian obtained via a Schrieffer--Wolff transformation, only second-order tunneling processes survive, connecting states through single polaron tunneling events with matrix elements proportional to $h_x^2$. The associated energy changes $\Delta E$ are shown next to each process, along with the effective tunneling amplitudes. Creation and annihilation of polarons are energetically suppressed, as indicated by red crosses. (b) Additional domain wall types observed in quantum simulation. Black arrows mark the most likely tunnelling events that occur within the domain wall, with intermediate virtual states involving polaron annihilation ($\Delta E_h$) or creation ($\Delta E_p$). Energy costs vary due to local spin environments, illustrating the microscopic diversity of domain wall motion.
• Figure 3: Quantum simulation of domain-wall dynamics on a superconducting quantum annealer. (a) Embedding of a triangular lattice with $N_\mathrm{L}=2008$ logical sites into the quantum annealer using $N_\mathrm{P}=2673$ physical qubits. Each square plaquette of four physical qubits represents a building block triangle of the logical lattice, resulting in a physical-to-logical qubit ratio of $4/3$. Inset: detailed view of the embedding. (b) Schematic of the embedding couplings. Black links denote antiferromagnetic Ising couplings ($J>0$) that map onto the edges of the logical triangular lattice. Red links indicate strong ferromagnetic embedding couplings ($J_\mathrm{emb}<0$) that bind pairs of physical qubits into a single logical qubit by enforcing identical spin states. (c) Energy scales of the quantum annealer Hamiltonian as functions of the annealing schedule parameter $s$. The transverse-field term $A(s)$ and the Ising term $B(s)$ are shown in units of GHz$/h$, where $h$ is Planck’s constant. (d) Reverse annealing protocol used to generate relaxation dynamics. Starting from a classical configuration at $s=1$ ($h_x=0$), the transverse field is ramped to a target value corresponding to the desired $h_x=1/r$ over an annealing time $t_a=5~\mu s$ and then ramped back to $s=1$. The final configuration of each reverse anneal is used as the initial configuration for the next cycle, producing a discrete-time dynamical evolution analogous to time-resolved STM measurements.
• Figure 4: Scaling collapse of reconfiguration rates and noise-dominated dynamics. (a) Average reconfiguration rate as a function of effective temperature $T_\mathrm{eff}$ for several transverse-field strengths $h_x$, showing a smooth crossover from weakly temperature-dependent dynamics at low $T_\mathrm{eff}$ to rapidly increasing activity at higher $T_\mathrm{eff}$. The dependence on $h_x$ is comparatively weak, with only a modest shift of the crossover. (b) Scaling collapse of the same data obtained by rescaling the temperature axis as $T_\mathrm{eff}\rightarrow h_x^{0.2}T_\mathrm{eff}$. The near-collapse across more than an order of magnitude in rate indicates that the reconfiguration dynamics depend only weakly on $h_x$, inconsistent with a tunnelling-dominated scaling $\propto h_x^2$ or higher order processes. (c) Schematic of elementary reconfiguration processes on the effective triangular lattice. Large apparent domain-wall rearrangements arise from cascades of local single-polaron tunnelling events (dashed arrows) rather than collective multi-polaron tunnelling. (d) Corresponding schematic for the experimental system, illustrating that extended rearrangements of CDW domain walls are composed of sequences of local polaron moves within the domain-wall network. Despite differences in global charge evolution between simulation and experiment, the microscopic reconfiguration mechanisms at domain walls are the same in both systems.