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1. Deconfined quantum criticality of nodal d -wave superconductivity, Néel order, and charge order on the square lattice at half-filling

   https://doi.org/10.1103/PhysRevResearch.6.033018  

   Christos, Maine ; Shackleton, Henry ; Sachdev, Subir ; Luo, Zhu-Xi ( July 2024 , Physical Review Research)

   We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the$\pi$-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background$\pi$-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal$d$-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by$(2+1)$-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional$d$-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases.

   Published by the American Physical Society2024 

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2. Spin-Peierls instability of the U(1) Dirac spin liquid

   https://doi.org/10.1038/s41467-024-51367-w  

   Seifert, Urban_F_P ; Willsher, Josef ; Drescher, Markus ; Pollmann, Frank ; Knolle, Johannes ( August 2024 , Nature Communications)

   Quantum fluctuations can inhibit long-range ordering in frustrated magnets and potentially lead to quantum spin liquid (QSL) phases. A prime example are gapless QSLs with emergent U(1) gauge fields, which have been understood to be described in terms of quantum electrodynamics in 2+1 dimension (QED₃). Despite several promising candidate materials, however, a complicating factor for their realisation is the presence of other degrees of freedom. In particular lattice distortions can act to relieve magnetic frustration, precipitating conventionally ordered states. In this work, we use field-theoretic arguments as well as extensive numerical simulations to show that the U(1) Dirac QSL on the triangular and kagome lattices exhibits a weak-coupling instability due to the coupling of monopoles of the emergent gauge field to lattice distortions, leading to valence-bond solid ordering. This generalises the spin-Peierls instability of one-dimensional quantum critical spin chains to two-dimensional algebraic QSLs. We study static distortions as well as quantum-mechanical phonons. Even in regimes where the QSL is stable, the singular spin-lattice coupling leads to marked temperature-dependent corrections to the phonon spectrum, which provide salient experimental signatures of spin fractionalisation. We discuss the coupling of QSLs to the lattice as a general tool for their discovery and characterisation.

    

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3. A model of d -wave superconductivity, antiferromagnetism, and charge order on the square lattice

   https://doi.org/10.1073/pnas.2302701120  

   Christos, Maine ; Luo, Zhu-Xi ; Shackleton, Henry ; Zhang, Ya-Hui ; Scheurer, Mathias S. ; Sachdev, Subir ( May 2023 , Proceedings of the National Academy of Sciences)

   We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory ofN_f= 2 massless Dirac fermions carrying fundamental gauge charges—this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice withπ-flux per plaquette in the ℤ₂center of SU(2). This theory has an emergent SO(5)_fglobal symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsionUat half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving inπℤ₂-flux. At half-filling, the low-energy theory of the Higgs sector hasN_b= 2 relativistic bosons with a possible emergent SO(5)_bglobal symmetry describing rotations between ad-wave superconductor, period-2 charge stripes, and the time-reversal breaking “d-density wave” state. We propose a conformal SU(2) gauge theory withN_f= 2 fundamental fermions,N_b= 2 fundamental bosons, and a SO(5)_f×SO(5)_bglobal symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)_fand a confining state which breaks SO(5)_b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order andd-wave superconductivity. A similar theory applies at nonzero doping and largeU, with longer-range couplings of the chargons leading to charge order with longer periods.

    

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4. Anderson–Kitaev spin liquid

   https://doi.org/10.1038/s41535-020-00285-3  

   Yamada, Masahiko G. ( November 2020 , npj Quantum Materials)

   The bond-disordered Kitaev model attracts much attention due to the experimental relevance inα-RuCl₃andA₃LiIr₂O₆(A= H, D, Ag, etc.). Applying a magnetic field to break the time-reversal symmetry leads to a strong modulation in mass terms for Dirac cones. Because of the smallness of the flux gap of the Kitaev model, a small bond disorder can have large influence on itinerant Majorana fermions. The quantization of the thermal Hall conductivityκ^xy/Tdisappears by a quantum Hall transition induced by a small disorder, andκ^xy/Tshows a rapid crossover into a state with a negligible Hall current. We call this immobile liquid state Anderson–Kitaev spin liquid (AKSL). Especially, the critical disorder strengthδJ_c1~ 0.05 in the unit of the Kitaev interaction would have many implications for the stability of Kitaev spin liquids.

    

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5. Gapped magnetic ground state in quantum spin liquid candidate κ-(BEDT-TTF) 2 Cu 2 (CN) 3

   https://doi.org/10.1126/science.abc6363  

   Miksch, Björn ; Pustogow, Andrej ; Rahim, Mojtaba Javaheri ; Bardin, Andrey A. ; Kanoda, Kazushi ; Schlueter, John A. ; Hübner, Ralph ; Scheffler, Marc ; Dressel, Martin ( April 2021 , Science)

   Geometrical frustration, quantum entanglement, and disorder may prevent long-range ordering of localized spins with strong exchange interactions, resulting in an exotic state of matter. κ-(BEDT-TTF)₂Cu₂(CN)₃is considered the prime candidate for this elusive quantum spin liquid state, but its ground-state properties remain puzzling. We present a multifrequency electron spin resonance (ESR) study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at 6 kelvin. This opening of a spin gap, accompanied by structural modifications, is consistent with the formation of a valence bond solid ground state. We identify an impurity contribution to the ESR response that becomes dominant when the intrinsic spins form singlets. Probing the electrons directly manifests the pivotal role of defects for the low-energy properties of quantum spin systems without magnetic order.

    

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