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arXiv:1304.4938 · Europhysics Letters (EPL)

Deconfined quantum criticality and conformal phase transition in two-dimensional antiferromagnets

Flavio S. Nogueira, Asle Sudbø

Published Dec 1, 2013• 19 citations
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Abstract

Deconfined quantum criticality of two-dimensional $SU(2)$ quantum antiferromagnets featuring a transition from an antiferromagnetically ordered ground state to a so-called valence-bond solid state, is governed by a non-compact CP$^1$ model with a Maxwell term in 2+1 spacetime dimensions. We introduce a new perspective on deconfined quantum criticality within a field-theoretic framework based on an expansion in powers of $ε=4-d$ for fixed number $N$ of complex matter fields. We show that in the allegedly weak first-order transition regime, a so-called conformal phase transition leads to a genuine deconfined quantum critical point. In such a transition, the gap vanishes when the critical point is approached from above and diverges when it is approached from below. We also find that the spin stiffness has a universal jump at the critical point.

DOI
10.1209/0295-5075/104/56004

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Deconfined quantum criticality of two-dimensional SU(2)SU(2)SU(2) quantum antiferromagnets featuring a transition from an antiferromagnetically ordered ground state to a so-called valence-bond solid state, is governed by a non-compact CP1^11 model with a Maxwell term in 2+1 spacetime dimensions. We introduce a new perspective on deconfined quantum criticality within a field-theoretic framework based on an expansion in powers of ε=4−dε=4-dε=4−d for fixed number NNN of complex matter fields. We show that in the allegedly weak first-order transition regime, a so-called conformal phase transition leads to a genuine deconfined quantum critical point. In such a transition, the gap vanishes when the critical point is approached from above and diverges when it is approached from below. We also find that the spin stiffness has a universal jump at the critical point.
The deconfined quantum critical point (DQCP) -- the enigmatic incarnation of the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm of symmetries and their spontaneous breaking -- has been proposed and actively pursued for more than two decades. Various 2D quantum many-body lattice models, both in spin/boson and fermion representations have been tested with the state-of-the-art numerical techniques and field-theoretical analyses, and yet, the conclusion is still controversial. Experimental realizations of DQCP in the quantum magnet SrCu2_22​(BO3_33​)2_22​ and superconducting quantum criticality in 2D material have either shown first order transition or intermediate phase. The tension between the lattice scale details and the requirement from continuum limit, manifested in the form of the inconsistent critical scaling behavior and violations of generic conformal bootstrap bound, has not been resolved. Here we solve these decades-long controversies from the new and fundamental perspective of the quantum entanglement. We develop the incremental algorithm to compute the entanglement entropy at a fermionic DQCP with unprecedentedly accurate data and reveal the universal coefficient of the logarithmic correction therein is negative and at odds with positivity requirement of the conformal field theory. Together with results in other 2D DQCP lattice models (both in fermion and spin systems), our discoveries clearly demonstrate the 2D SU(2) antiferromagnet to valence bond solid DQCPs are not conformal fixed point and naturally explain the experimental difficulties in finding them. This marks the end of the beginning of unambiguous finding of the quantum phase transitions truely beyond the Landau-Ginzburg-Wilson paradigm, since its suggestion two decades ago.
The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S=1/2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations. The results support a continuous transition of the ground state, in agreement with the theory of "deconfined" quantum criticality. There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated. This suggests that either the SU(N) symmetric noncompact CP;{N-1} field theory for deconfined quantum criticality has to be revised or that the theory for N=2 (as in the system studied here) differs significantly from N-->infinity (where the field theory is analytically tractable).
It has been proposed that the deconfined criticality in (2+1)d(2+1)d(2+1)d---the quantum phase transition between a N\'eel antiferromagnet and a valence-bond solid (VBS)---may actually be pseudocritical, in the sense that it is a weakly first-order transition with a generically long correlation length. The underlying field theory of the transition would be a slightly complex (nonunitary) fixed point as a result of fixed points annihilation. This proposal was motivated by existing numerical results from large scale Monte Carlo simulations as well as a conformal bootstrap. However, an actual theory of such a complex fixed point, incorporating key features of the transition such as the emergent SO(5) symmetry, is so far absent. Here we propose a Wess-Zumino-Witten (WZW) nonlinear sigma model with level k=1k=1k=1, defined in $2+\ensuremath{\epsilon}$ dimensions, with target space ${S}^{3+\ensuremath{\epsilon}}$ and global symmetry $\text{SO}(4+\ensuremath{\epsilon})$. This gives a formal interpolation between the deconfined criticality at d=3d=3d=3 and the SU(2)1\text{SU}{(2)}_{1}SU(2)1​ WZW theory at d=2d=2d=2 describing the spin-1/21/21/2 Heisenberg chain. The theory can be formally controlled, at least to leading order, in terms of the inverse of the WZW level 1/k1/k1/k. We show that at leading order there is a fixed point annihilation at ${d}^{*}\ensuremath{\approx}2.77$, with complex fixed points above this dimension including the physical d=3d=3d=3 case. The pseudocritical properties such as correlation length, scaling dimensions, and the drifts of scaling dimensions as the system size increases, calculated crudely to leading order, are qualitatively consistent with existing numerics.
We resolve the nature of the quantum phase transition between antiferromagnetic and valence-bond solid ground states in square-lattice spin-1/2 magnets - the putative deconfined quantum-critical point. Using quantum Monte Carlo simulations of J-Q models, in which Heisenberg exchange J competes with multi-spin interactions Qn formed by n singlet projectors, we demonstrate first-order discontinuities increasing with n. For n=2 and n=3, the first-order signatures are very weak and we extract universal scaling dimensions of a proximate multicritical point. Their values coincide closely with known bounds for an SO(5) symmetric conformal field theory (CFT) containing a relevant SO(5) singlet operator that destabilizes the generic deconfined critical point. We characterize the emergent SO(5) symmetry by its scaling dimensions of the leading irrelevant perturbations. Using the J-Q2-Q6 model, we tune the transition from weak to stronger first-order and find scaling of the coexisting order parameters with a large exponent beta ~ 0.85, in agreement with the relevant scaling dimensions of the multicritical point. The exponent that had previously been identified with the correlation length does not have a corresponding CFT level, and we explain it as pseudo-critical length scale of bubbles of one phase inside the other that are compressed in size by an SO(5)-violating irrelevant repulsive interaction between the two order parameters. The bubble scale reflects a hierarchy of excitation gaps generated by the SO(5) perturbation in the neighborhood of the first-order transition, akin to a Higgs mechanism. We argue that the multicritical point is the tip of a gapless spin liquid phase in frustrated Heisenberg models into which the J-Q models can be deformed, but the spin liquid, and perhaps the multicritical point itself, exist outside the regime amenable to sign-free simulations.
Two-dimensional quantum antiferromagnets are believed to host phases of matter whose excitations are more fundamental than those of the ordered phases. When combining two such spin systems in a bilayer, strong interaction between the emergent excitations can produce phases not realized in either of its subsystems. We show that the critical fluctuations of a two-dimensional spin-liquid state can induce a deconfined quantum critical point in a proximate antiferromagnet. The most relevant coupling between the associated effective field theories is given by a mixed Chern-Simons term of the emergent gauge fields in each layer. This describes a topological current-current interaction. In contrast to the local spin-spin interaction, it strongly modifies the renormalization group flow of the theory describing the N\'eel--valence-bond-solid transition of the antiferromagnet. In particular, the protected coupling constant associated with it implies nontrivial quantum critical scaling characterized by a nonuniversal power-law divergence of the correlation length in the critical domain and Berezinskii-Kosterlitz-Thouless divergence approaching it.
The S=1/2 square-lattice J-Q model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model-a term projecting staggered singlets, as well as a modulation of the J terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point-the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method.