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Register a new userCritical properties of the valence-bond-solid transition in lattice quantum electrodynamics
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Elucidating the phase diagram of lattice gauge theories with fermionic matter in 2+1 dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in high-energy physics to fractionalized phases of strongly correlated materials in condensed matter physics. For a sufficiently large number $N_f$ of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (QED$_3$) on the square lattice have found evidence for a continuous quantum phase transition between a power-law correlated conformal QED$_3$ phase and a confining valence-bond-solid phase with spontaneously broken point-group symmetries. The critical continuum theory of this transition was shown to be the $O(2)$ QED$_3$-Gross-Neveu model, equivalent to the gauged Nambu-Jona-Lasinio model, and critical exponents were computed to first order in the large-$N_f$ expansion and the $epsilon$ expansion. We extend these studies by computing critical exponents to second order in the large-$N_f$ expansion and to four-loop order in the $epsilon$ expansion below four spacetime dimensions. In the latter context, we also explicitly demonstrate that the discrete $mathbb{Z}_4$ symmetry of the valence-bond-solid order parameter is dynamically enlarged to a continuous $O(2)$ symmetry at criticality for all values of $N_f$.
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Recent sign-problem-free quantum Monte Carlo simulations of (2+1)-dimensional lattice quantum electrodynamics (QED$_3$) with $N_f$ flavors of fermions on the square lattice have found evidence of continuous quantum phase transitions between a critical phase and a gapped valence-bond-solid (VBS) phase for flavor numbers $N_f=4$, $6$, and $8$. We derive the critical theory for these transitions, the chiral $O(2)$ QED$_3$-Gross-Neveu model, and show that the latter is equivalent to the gauged Nambu--Jona-Lasinio model. Using known large-$N_f$ results for the latter, we estimate the order parameter anomalous dimension and the correlation length exponent for the transitions mentioned above. We obtain large-$N_f$ results for the dimensions of fermion bilinear operators, in both the gauged and ungauged chiral $O(2)$ Gross-Neveu models, which respectively describe the long-distance power-law decay of two-particle correlation functions at the VBS transition in lattice QED$_3$ and the Kekule-VBS transition for correlated fermions on the honeycomb lattice.
The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED$_3$), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $pi$-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U(1) gauge field on the square lattice have shown that quantum fluctuations can destroy Neel order and drive a direct quantum phase transition to the $pi$-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED$_3$-Gross-Neveu-Yukawa model with a single SU(2) doublet of four-component Dirac fermions (i.e., $N_f=1$), pointing out important differences with the corresponding putative transition on the kagome lattice. Using an $epsilon$ expansion below four spacetime dimensions to four-loop order, and a large-$N_f$ expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-Neel transition for interacting fermions on the honeycomb lattice.
A molecular Mott insulator $kappa$-(ET)$_2$B(CN)$_4$ [ET = bis(ethylenedithio)tetrathiafulvalene] with a distorted triangular lattice exhibits a quantum disordered state with gapped spin excitation in the ground state. $^{13}$C nuclear magnetic resonance, magnetization, and magnetic torque measurements reveal that magnetic field suppresses valence bond order and induces long-range magnetic order above a critical field $sim 8$ T. The nuclear spin-lattice relaxation rate $1/T_1$ shows persistent evolution of antiferromagnetic correlation above the transition temperature, highlighting a quantum spin liquid state with fractional excitations. The field-induced transition as observed in the spin-Peierls phase suggests that the valence bond order transition is driven through renormalized one-dimensionality and spin-lattice coupling.
We study a one-dimensional (1d) system that shows many analogies to proposed two-dimensional (2d) deconfined quantum critical points (DQCP). Our system is a translationally invariant spin-1/2 chain with on-site $Z_2 times Z_2$ symmetry and time reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the $Z_2$ symmetries and the time reversal are broken, to a valence bond solid (VBS), where all on-site symmetries are restored while the translation symmetry is broken. The other $Z_2$ symmetry remains unbroken throughout, but its presence is crucial for both the direct transition (via specific Berry phase effect on topological defects, also related to a Lieb-Schultz-Mattis-like theorem) and the precise characterization of the VBS phase (which has crystalline-SPT-like property). The transition has a description in terms of either two domain wall species that fractionalize the VBS order parameter or in terms of partons that fractionalize the FM order parameter, with each picture having its own $Z_2$ gauge structure. The two descriptions are dual to each other and, at long wavelengths, take the form of a self-dual emph{gauged} Ashkin-Teller model, reminiscent of the self-dual easy-plane non-compact CP$^1$ model that arises in the description of the 2d easy-plane DQCP. We also find an exact reformulation of the transition that leads to a simple field theory description that explicitly unifies the FM and VBS order parameters; this reformulation can be interpreted as a new parton approach that does not attempt to fractionalize either of the two order parameters but instead encodes them in instantons. Besides providing explicit realizations of many ideas proposed in the context of the 2d DQCP, here in the simpler and fully tractable 1d setting with continuous transition, our study also suggests possible new line of approach to the 2d DQCP.
We present numerical evidence for the emergence of an extended valence bond solid (VBS) phase at $T=0$ in the kagome $S=1/2$ Heisenberg antiferromagnet with ferromagnetic further-neighbor interactions. The VBS is located at the boundary between two magnetically ordered regions and extends close to the nearest-neighbor Heisenberg point. It exhibits a diamond-like singlet covering pattern with a $12$-site unit-cell. Our results suggest the possibility of a direct, possibly continuous, quantum phase transition from the neighboring $mathbf{q}=0$ coplanar magnetically ordered phase into the VBS phase. Moreover, a second phase which breaks lattice symmetries, and is of likely spin-nematic type, is found close to the transition to the ferromagnetic phase. The results have been obtained using numerical Exact Diagonalization. We discuss implications of our results on the nature of nearest-neighbor Heisenberg antiferromagnet.
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