Boson-doped Mott Antiferromagnets Exhibit Six Phases, Including a Pair Density Wave State at Low Doping

The behaviour of interacting particles in materials often gives rise to unexpected and complex states of matter, and recent advances in manipulating cold atoms now allow physicists to explore these phenomena with unprecedented control. Xin Lu, Jia-Xin Zhang, and Lukas Homeier, along with colleagues including Hong-Chen Jiang, Shou-Shu Gong, and D. N. Sheng, investigate a model system of interacting bosons arranged on a square lattice, revealing a surprising landscape of competing orders. Their large-scale simulations demonstrate six distinct phases, extending far beyond the simple, expected behaviour of these particles, and uncover a novel pair density wave phase where doped holes bind together at low concentrations. The team also predicts the emergence of both spatially separated ferromagnetic and antiferromagnetic regions, and proposes a practical scheme to realise these states using Rydberg atoms, offering new insights into the complex interplay between charge and spin that may underpin high-temperature superconductivity.

Resonant Rare Regions Drive MBL Breakdown

Inspired by recent experimental advances in quantum simulation, this work investigates the breakdown of many-body localization (MBL) in a disordered three-dimensional system. Researchers demonstrate that rare, spatially resonant quantum states can provide a pathway for thermalization, even when conventional dephasing mechanisms are absent. Through numerical simulations employing both exact diagonalization and time-dependent variational principle methods, the team characterised how these resonances emerge and influence the system’s behaviour. The simulations reveal that the MBL phase becomes unstable as system size increases, with its lifetime decreasing approximately as the inverse square of the linear system size.

These findings suggest that the resonances, arising from the interplay between disorder and interactions, limit the stability of the MBL phase in three dimensions. Analysis of the energy levels shows a transition from a distribution characteristic of localized states to one indicative of thermalization as the system approaches a critical point. Furthermore, the team quantified the growth of entanglement during thermalization events, finding it saturates at a value consistent with a fully thermalized system. Varying the strength of the disorder revealed that stronger disorder suppresses these resonances and extends the lifetime of the MBL phase, although this effect is limited by the size of the simulated systems. While these simulations are limited to relatively small systems, they provide valuable insights into the potential instability of MBL in higher dimensions.

Rydberg Arrays for Tunable Strong Interactions

This research details a theoretical and experimental proposal for creating a tunable Hubbard model with strong interactions using arrays of Rydberg atoms. The goal is to establish a platform for studying strongly correlated quantum systems, specifically achieving a wide range of parameters, including tunable next-nearest-neighbor hopping. The proposal outlines how to control interactions and hopping terms using precisely controlled Rydberg atom interactions in optical tweezers, and how to tune the ratio of next-nearest-neighbor to nearest-neighbor hopping by manipulating the array geometry and laser polarization. This approach offers unprecedented control over quantum interactions and opens new avenues for exploring complex quantum phenomena.

The research focuses on realizing the Hubbard model, a fundamental framework for describing interacting electrons in a lattice. The team aims to explore the strongly correlated regime, where electron-electron interactions dominate, leading to exotic quantum phases. A key goal is to achieve a tunable ratio of next-nearest-neighbor hopping to nearest-neighbor hopping, a crucial parameter for exploring different quantum phases and phase transitions. The experimental platform utilizes Rydberg atoms, which exhibit strong, long-range interactions due to their large dipole moments, trapped in optical tweezers.

By controlling the laser frequency and intensity, the strength of these interactions can be precisely tuned. The team’s approach involves manipulating the geometry of the lattice and distorting it along one direction, creating an anisotropic lattice where the spacing between atoms differs in two directions. The polarization of the laser driving the Rydberg excitation controls the sign and strength of the hopping terms, and a mathematical transformation effectively switches the sign of the hopping terms, allowing for both positive and negative values. The ratio of next-nearest-neighbor to nearest-neighbor hopping is tuned by varying the angle of lattice distortion and the laser polarization. This detailed plan provides a pathway for building a highly controllable quantum simulator with unprecedented control over quantum interactions.

Pair Density Waves and Doping Effects

This work presents a comprehensive investigation of the bosonic t-t′-J model on a square lattice, utilizing large-scale density matrix renormalization group simulations to map out its quantum phase diagram. Researchers explored the model by tuning both the doping level and the hopping ratio between sites, revealing a rich landscape of unconventional phases beyond simple superfluidity. The team systematically varied doping from 1/24 to 1/3, while exploring a range of next-nearest-neighbor hopping amplitudes, to comprehensively chart the system’s behaviour. These findings provide valuable insights into the complex interplay between doping, hopping, and magnetic order in these materials.

At low doping levels, the simulations identified a pair density wave (PDW) phase, characterized by tightly bound pairs of doped holes condensing into a spatially modulated pattern atop an antiferromagnetic spin background. As doping increases, the system transitions into a superfluid phase exhibiting in-plane xy-ferromagnetic order, where doped holes condense at the momentum (0, 0). These two phases are connected by an intermediate region, demonstrating a continuous evolution of quantum states with increasing doping. Introducing next-nearest-neighbor hopping significantly alters the phase diagram, leading to the discovery of a disordered pair density wave (dPDW) phase lacking both single-boson and pair coherence.

Additionally, an exotic superfluid (SF*) phase was identified, characterized by condensation at emergent incommensurate momenta concurrent with incommensurate magnetic order, demonstrating a novel form of quantum coherence. To facilitate future experimental realization, the researchers proposed a concrete scheme using Rydberg tweezer arrays to realize both positive and negative values of the next-nearest-neighbor hopping. This scheme provides a direct mapping between model parameters and experimentally accessible regimes, paving the way for validating the theoretical predictions. This work provides a solid theoretical foundation for future Rydberg tweezer experiments and advances understanding of doped antiferromagnets, with implications for high-temperature superconductivity.

Doped Antiferromagnets Exhibit Exotic Quantum Phases

This research presents a detailed investigation of the bosonic t-t′-J model, a theoretical framework used to understand doped antiferromagnetic materials, using large-scale computational simulations. By systematically varying the doping level and the relative strength of hopping terms, scientists have mapped out a complex phase diagram revealing several unconventional quantum phases beyond simple superfluidity. These include a pair density wave phase, characterized by spatially modulated pairing of particles, and a disordered pair density wave phase lacking long-range coherence. Notably, the team also identified an exotic superfluid phase exhibiting condensation at unexpected, incommensurate momenta.

These findings significantly expand understanding of how doped holes interact within antiferromagnetic systems, potentially offering insights relevant to high-temperature superconductivity. The research demonstrates that the interplay between particle interactions and hopping dynamics can give rise to a rich landscape of emergent quantum phases. Future work will focus on exploring larger system sizes and different geometries to confirm these findings and investigate the potential for novel quantum phenomena. Furthermore, the team proposes a concrete experimental realization of this model using Rydberg tweezer arrays, paving the way for direct observation and manipulation of these exotic quantum states.