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Theoretical high-energy and condensed-matter physics share various ideas and tools. New connections between the two have been established through quantum information, providing exciting prospects for theoretical advances and even potential experimental studies. Six scientists discuss different directions of research in this inter-disciplinary field.

Digital quantum simulations of Kitaev’s honeycomb model are realized for two-dimensional fermionic systems using a reconfigurable atom-array processor and used to study the Fermi–Hubbard model on a square lattice.

Although the concept of a quasiparticle—a particle plus interactions—works very well for some problems, in other cases quasiparticles can be destroyed by quantum fluctuations. Alternative theoretical techniques for handling strong interactions are needed, such as those from string theory.

The discovery of a new class of high-temperature superconductors based on iron tests the limits of current theoretical and computational tools for the understanding of strongly correlated systems.

A programmable quantum simulator based on Rydberg atom arrays is used to study the collective dynamics of a quantum phase transition and observe the phenomenon of quantum coarsening.

There are two distinct types of particles in nature: fermions and bosons. But it seems bosons may assume similar characteristics to fermion systems in the low-temperature regime typical of Bose–Einstein condensation.

Quantum dimer models are known to host topological quantum spin liquid phases, and it has recently become possible to simulate related \({{\mathbb{Z}}}_{2}\) gauge theories with Rydberg atoms. Yan et al. compute the phase diagram of an experimentally motivated quantum dimer model on a triangular lattice with fluctuating dimer density.

A quantum spin liquid is a spin state with no magnetic order even at the lowest temperatures. To explain neutron scattering data on a ‘kagome lattice’ antiferromagnet, visons (elementary excitations of vortices) must be included, in addition to the usual fractionalized spinons.

The remarkably large thermal Hall response recently observed in the copper oxides challenges our understanding of the excitations in an insulating antiferromagnet. Here, a possible explanation of the underlying physics is provided.

The authors theoretically study superconductivity in twisted-bilayer and twisted-trilayer graphene, finding that flavor polarization allows for Cooper pairing in which the pairs consist of electrons in different bands. Both intervalley phonons and fluctuations of a time-reversal-symmetric intervalley coherent order can favor such pairing.

The nature of the so-called pseudogap phase exhibited by many cuprate superconductors is one of the most puzzling questions in the field of unconventional superconductivity. Allais et al. present a model that can reconcile some of the experimental observations at high and low fields.

A Rydberg atom quantum simulator with programmable interactions is used to experimentally verify the quantum Kibble–Zurek mechanism through the growth of spatial correlations during quantum phase transitions.

A programmable quantum simulator with 256 qubits is created using neutral atoms in two-dimensional optical tweezer arrays, demonstrating a quantum phase transition and revealing new quantum phases of matter.

Quantum magnetism describes systems of magnetic spins in which quantum mechanical effects dominate, often in surprising ways. This review article covers phase transitions between these states, including quantum criticality and entangled electron states.

By using the sweeping cluster quantum Monte Carlo algorithm, the authors reveal the complete ground-state phase diagram of the triangular-lattice fully packed quantum loop model. They discover a hidden vison plaquette phase between the known lattice nematic solid and the even \({{\mathbb{Z}}}_{2}\) quantum spin liquid (QSL) phase, which had been previously misinterpreted as the QSL, and explain how to detect it experimentally.