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 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. *

We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1 < 0 (nearest neighbor, ferromagnetic) and J2 > 0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g = J2/|J1| > 1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2 < g < g * , where g * = 0.67 ± 0.01. Thereafter, the transitions from g = g * to g → ∞ are continuous and can be fully mapped, using universality arguments, to the critical line of the well known Ashkin-Teller model from its 4-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the AshkinTeller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g * in the J1-J2 model. The continuous transitions near g * can therefore be mistaken to be first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g > 1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological bench-marks for weakly first-order behaviors and Ashkin-Teller criticality.

We investigate the hard-square lattice-gas model by means of transfer-matrix calculations and a finite-sizescaling analysis. Using a minimal set of assumptions we find that the spectrum of correction-to-scaling exponents is consistent with that of the exactly solved Ising model, and that the critical exponents and correlationlength amplitudes closely follow the relation predicted by conformal invariance. Assuming that these spectra are exactly identical, and conformal invariance, we determine the critical point, the conformal anomaly, and the temperature and magnetic exponents with numerical margins of 10 Ϫ11 or less. These results are in a perfect agreement with the exactly known Ising universal parameters in two dimensions. In order to obtain this degree of precision, we included system sizes as large as feasible, and used extended-precision floating-point arithmetic. The latter resource provided a substantial improvement of the analysis, despite the fact that it restricted the transfer-matrix calculations to finite sizes of at most 34 lattice units.

Surface critical behavior (SCB) refers to the singularities of physical quantities on the surface at the bulk phase transition. It is closely related to and even richer than the bulk critical behavior. In this work, we show that three types of SCB universality are realized in the dimerized Heisenberg models at the (2+1)-dimensional O(3) quantum critical points by engineering the surface configurations. The ordinary transition happens if the surface is gapped in the bulk disordered phase, while the gapless surface state generally leads to the multicritical special transition, even though the latter is precluded in classical phase transitions because the surface is in the lower critical dimension. An extraordinary transition is induced by the ferrimagnetic order on the surface of the staggered Heisenberg model, in which the surface critical exponents violate the results of the scaling theory and thus seriously challenge our current understanding of extraordinary transitions.

The discovery of quantum spin-Hall (QSH) insulators has brought topology to the forefront of condensed matter physics. While a QSH state from spin-orbit coupling can be fully understood in terms of band theory, fascinating many-body effects are expected if it instead results from spontaneous symmetry breaking. Here, we introduce a model of interacting Dirac fermions where a QSH state is dynamically generated. Our tuning parameter further allows us to destabilize the QSH state in favour of a superconducting state through proliferation of charge-2e topological defects. This route to superconductivity put forward by Grover and Senthil is an instance of a deconfined quantum critical point (DQCP). Our model offers the possibility to study DQCPs without a second length scale associated with the reduced symmetry between field theory and lattice realization and, by construction, is amenable to large-scale fermion quantum Monte Carlo simulations.

We report high-pressure magnetization and 35 Cl NMR studies on α-RuCl3 with pressure up to 1.5 GPa. At low pressures, the magnetic ordering is identified by both the magnetization data and the NMR data, where the TN shows a concave shape dependence with pressure. These data suggest stacking rearrangement along the c-axis. With increasing pressure, phase separation appears prominently at P ≥ 0.45 GPa, and the magnetic volume fraction is completely suppressed at P ≥ 1.05 GPa. Meanwhile, a phase-transition-like behavior emerges at high pressures in the remaining volume by a sharp drop of magnetization M (T ) upon cooling, with the transition temperature Tx increased to 250 K at 1 GPa. The 1/ 35 T1 is reduced by over three orders of magnitude when cooled below 100 K. This characterizes a high-pressure, low-temperature phase with nearly absent static susceptibility and low-energy spin fluctuations. The nature of the high-pressure ground state is discussed, where a magnetically disordered state is proposed as a candidate state.

No abstract