The theory of deconfined quantum critical points describes phase transitions at temperature T = 0 outside the standard paradigm, predicting continuous transformations between certain ordered states where conventional theory requires discontinuities. Numerous computer simulations have offered no proof of such transitions, however, instead finding deviations from expected scaling relations that were neither predicted by the DQC theory nor conform to standard scenarios. Here we show that this enigma can be resolved by introducing a critical scaling form with two divergent length scales. Simulations of a quantum magnet with antiferromagnetic and dimerized ground states confirm the form, proving a continuous transition with deconfined excitations and also explaining anomalous scaling at T > 0. Our findings revise prevailing paradigms for quantum criticality, with potentially far-reaching implications for many strongly-correlated materials. arXiv:1603.02171v2 [cond-mat.str-el] 27 Apr 2016Introduction In analogy with classical phase transitions driven by thermal fluctuations, condensed matter systems can undergo drastic changes as parameters regulating quantum fluctuations are tuned at low temperatures. Some of these quantum phase transitions can be theoretically understood as rather straight-forward generalizations of thermal phase transitions [1,2], where, in the conventional Landau-Ginzburg-Wilson (LGW) paradigm, states of matter are characterized by order parameters. Many strongly-correlated quantum materials seem to defy such a description, however, and call for new ideas.A promising proposal is the theory of deconfined quantum critical (DQC) points in certain two-dimensional (2D) quantum magnets [3,4], where the order parameters of the antiferromagnetic (Néel) state and the competing dimerized state (the valence-bond-solid, VBS) are not fundamental variables but composites of fractional degrees of freedom carrying spin S = 1/2.These spinons are condensed and confined, respectively, in the Néel and VBS state, and become deconfined at the DQC point separating the two states. Establishing the applicability of the still controversial DQC scenario would be of great interest in condensed matter physics, where it may play an important role in strongly-correlated systems such as the cuprate superconductors [5]. There are also intriguing DQC analogues to quark confinement and other aspects of high-energy physics, e.g., an emergent gauge field and the Higgs mechanism and boson [6].The DQC theory represents the culmination of a large body of field-theoretic works on VBS states and quantum phase transitions out of the Néel state [7,8,9,2,10]. The postulated SU(N ) symmetric non-compact (NC) CP N −1 action can be solved when N → ∞ [11, 5, 12] but nonperturbative numerical simulations are required to study small N . The most natural physical realizations of the Néel-VBS transition for electronic SU(2) spins are frustrated quantum magnets [9], which, however, are notoriously difficult to study numerically [13,14]. Other models ...
We study the spin-excitation spectrum (dynamic structure factor) of the spin-1=2 square-lattice Heisenberg antiferromagnet and an extended model (the J-Q model) including four-spin interactions Q in addition to the Heisenberg exchange J. Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with quantum Monte Carlo simulations, we can treat the sharp (δ-function) contribution to the structure factor expected from spin-wave (magnon) excitations, in addition to resolving a continuum above the magnon energy. Spectra for the Heisenberg model are in excellent agreement with recent neutron-scattering experiments on CuðDCOOÞ 2 · 4D 2 O, where a broad spectral-weight continuum at wave vector q ¼ ðπ; 0Þ was interpreted as deconfined spinons, i.e., fractional excitations carrying half of the spin of a magnon. Our results at ðπ; 0Þ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at q ¼ ðπ=2; π=2Þ (as also seen experimentally). We further investigate the reasons for the small magnon weight at ðπ; 0Þ and the nature of the corresponding excitation by studying the evolution of the spectral functions in the J-Q model. Upon turning on the Q interaction, we observe a rapid reduction of the magnon weight to zero, well before the system undergoes a deconfined quantum phase transition into a nonmagnetic spontaneously dimerized state. Based on these results, we reinterpret the picture of deconfined spinons at ðπ; 0Þ in the experiments as nearly deconfined spinons-a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile ðπ; 0Þ-magnon pole in the Heisenberg model and its depletion in the J-Q model, we introduce an effective model of the excitations in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy to the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model can reproduce the reduction of magnon weight and lowered excitation energy at ðπ; 0Þ in the Heisenberg model, as well as the energy maximum and smaller continuum at ðπ=2; π=2Þ. It can also account for the rapid loss of the ðπ; 0Þ magnon with increasing Q and the remarkable persistence of a large magnon pole at q ¼ ðπ=2; π=2Þ even at the deconfined critical point. The fragility of the magnons close to ðπ; 0Þ in the Heisenberg model suggests that various interactions that likely are important in many materials-e.g., longer-range pair exchange, ring exchange, and spin-phonon interactions-may also destroy these magnons and lead to even stronger spinon signatures than in CuðDCOOÞ 2 · 4D 2 O.
We study effects of disorder (quenched randomness) in a two-dimensional square-lattice S = 1/2 quantum spin system, the J-Q model with a multi-spin interaction Q supplementing the Heisenberg exchange J. In the absence of disorder the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks Z4 symmetry spontaneously, and in the presence of arbitrarily weak disorder it forms domains. Using quantum Monte Carlo simulations, we demonstrate two different kinds of such disordered VBS states. Upon dilution, a removed site in one sublattice forces a left-over localized spin in the opposite sublattice. These spins interact through the host system and always form AFM order. In the case of random J or Q interactions in the intact lattice, we find a different, spin-liquid-like state with no magnetic or VBS order but with algebraically decaying mean correlations. Here we identify localized spinons at the nexus of domain walls separating regions with the four different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, we argue that there is a strong tendency to singlet formation, because of the native pairing and relatively strong spinonspinon interactions mediated by the domain walls. Thus, the spinon groups are effectively isolated from each other and no long-range AFM order forms. The mean spin correlations decay as r −2 as a function of distance r. We propose that this state is a two-dimensional analogue of the well-known random singlet (RS) state in one dimension, though, in contrast to the latter, the dynamic exponent z here is finite. By studying quantum-critical scaling of the magnetic susceptibility, we find that z varies, taking the value z = 2 at the AFM-RS phase boundary and growing upon moving into the RS phase (thus causing a power-law divergent susceptibility). The RS state discovered here in a system without geometric frustration may correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr2CuTe1−xWxO6 for x in the range 0.2 − 0.5. *
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