Dynamical Matter Generates Crucial Interactions for Exotic Materials Without Complex Calculations

Lattice gauge theories (LGTs) offer a valuable approach to understanding confinement, topological order, and novel materials. Matjaž Kebrič from JILA and the Department of Physics, University of Colorado, Boulder, Colorado, USA, Fabian Döschl and Umberto Borla from the Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Germany, along with Jad C. Halimeh and colleagues from the Max Planck Institute of Quantum Optics, 85748 Garching, Germany, and further collaborators at the Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, have investigated how dynamical matter influences these theories. Their work reveals that coupling dynamical matter to gauge fields naturally generates significant plaquette interactions, even without explicitly including them in the initial Hamiltonian. This finding is significant because it circumvents a key theoretical and experimental limitation in LGT studies, potentially enabling the creation of exotic phases of matter and offering a pathway towards realising a topologically protected spin liquid with a substantial energy gap.

Lattice gauge theories (LGTs) are a theoretical framework used to study phenomena like confinement, where particles bind together, and topological order, crucial for understanding exotic states of matter.

Simulating these theories is computationally demanding, and experimentally realising the necessary multi-body interactions, particularly ‘plaquette’ terms, has proven challenging. This work demonstrates that dynamical matter, specifically hard-core bosons coupled to a Z2 LGT, can naturally generate sizable plaquette interactions without requiring them to be explicitly included in the system’s design.

Using a combination of density matrix renormalization group simulations and neural quantum state calculations on systems up to 20 × 20 lattice sites, researchers analysed the model across varying fillings and electric field strengths. The study reveals a significant plaquette expectation value, independent of system size, arising from the interaction between the matter and the gauge field, even in the absence of explicit plaquette terms in the initial Hamiltonian.

The observed values demonstrate that dynamical matter inherently induces these multi-body interactions, and calculations show a robust plaquette expectation value that persists regardless of lattice dimensions, indicating a fundamental property of the system. This induced interaction strength diminishes predictably with increasing electric field strength, providing a tunable parameter for controlling the system’s behaviour.

Analysis of the model at small coupling strengths further revealed signatures consistent with a confinement-deconfinement transition, a crucial phenomenon in lattice gauge theory. The ability to generate plaquette terms through dynamical matter is particularly significant for quantum simulators, as it removes the need for complex and challenging direct implementation of these interactions.

This enhancement of magnetic energy scales, facilitated by the dynamical matter, is critical for stabilising quantum spin liquids, particularly in systems lacking native plaquette interactions. The study demonstrates that a filling of dynamical matter is sufficient to generate states with finite plaquette terms, circumventing the need for their explicit inclusion in experimental setups.

Density matrix renormalization group (DMRG) simulations and neural quantum state (NQS) calculations underpin this work, allowing analysis of a two-dimensional (2+1D) Z2 lattice gauge theory coupled to U matter up to a system size of 20 × 20. DMRG, a variational method for finding the ground state of a quantum many-body system, was initially employed to establish a benchmark for the neural network approach and to probe the system’s properties at smaller scales.

To extend the analysis beyond the limitations of DMRG, NQS were implemented, representing a novel numerical approach capable of circumventing some of the challenges faced by both quantum Monte Carlo and traditional tensor networks. These states, parameterised by a neural network, demonstrate remarkable efficiency in representing highly entangled quantum states and their dynamical properties, enabling the investigation of larger system sizes inaccessible to DMRG alone.

The DMRG results served as crucial validation for the NQS calculations, ensuring the accuracy and reliability of the extended simulations. The Hamiltonian governing the system incorporates a hopping term, -t, which describes the movement of hard-core bosons between neighbouring lattice sites, alongside a chemical potential term, μ, used to control the boson filling.

A Z2 gauge field, τz, resides on the links between lattice sites, mediating interactions between the bosons, and an electric field term, -h, is introduced to explore its influence on the system’s behaviour. Scientists have long sought to understand the emergence of complex behaviour from simple interactions, and this work represents a step forward in simulating those conditions.

The challenge lies in accurately modelling LGTs, the theoretical framework describing phenomena like confinement and exotic states of matter known as spin liquids. This research offers a potentially transformative approach by demonstrating that dynamical matter itself can induce these complex interactions, specifically the crucial ‘plaquette’ terms, within the system.

The implications extend beyond fundamental physics, potentially informing the design of novel materials with tailored quantum properties. While the observed signatures of a confinement-deconfinement transition are promising, confirming this transition definitively requires scaling the simulations to much larger systems. Furthermore, the observed behaviour of ‘mesons’, particles mediating the interactions, needs further investigation with larger datasets to solidify claims of condensation. Looking ahead, this work could inspire new avenues for both theoretical and experimental research, and other groups might explore different types of matter and lattice structures to see if this self-inducing interaction effect is widespread.