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Register a new userNonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
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As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in the two-dimensional (2D) J-Q$_3$ model. We discover fascinating nonequilibrium scaling behaviors hinging on the process of fractionization and the dynamics of emergent symmetry associated with two length scales. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems.
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Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities, i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly-correlated quantum-matter systems: the one relating the easy-plane noncompact CP$^1$ model (NCCP$^1$) and noncompact quantum electrodynamics (QED) with two flavors ($N = 2$) of massless two-component Dirac fermions. The easy-plane NCCP$^1$ model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while $N=2$ noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work we present strong numerical support for the proposed duality. We realize the $N=2$ noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC, we study a planar version of the $S=1/2$ $J$-$Q$ spin Hamiltonian (a quantum XY-model with additional multi-spin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships.
We perform a numerical study of a spin-1/2 model with $mathbb{Z}_2 times mathbb{Z}_2$ symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by Landau-Ginzburg-Wilson symmetry-breaking theory.
We propose a method to study dynamical response of a quantum system by evolving it with an imaginary-time dependent Hamiltonian. The leading non-adiabatic response of the system driven to a quantum-critical point is universal and characterized by the same exponents in real and imaginary time. For a linear quench protocol, the fidelity susceptibility and the geometric tensor naturally emerge in the response functions. Beyond linear response, we extend the finite-size scaling theory of quantum phase transitions to non-equilibrium setups. This allows, e.g., for studies of quantum phase transitions in systems of fixed finite size by monitoring expectation values as a function of the quench velocity. Non-equilibrium imaginary-time dynamics is also amenable to quantum Monte Carlo (QMC) simulations, with a scheme that we introduce here and apply to quenches of the transverse-field Ising model to quantum-critical points in one and two dimensions. The QMC method is generic and can be applied to a wide range of models and non-equilibrium setups.
We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a non-zero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large $M$ analysis of a model which extends the SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.
Noethers theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noethers theorem at the deconfined quantum critical point (DQCP), which is the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to emerged conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectra, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. Our study demonstrates an elegant yet practical approach to detect emergent symmetry by probing the spin excitations, which could potentially guide the ongoing experimental search for DQCP in quantum magnets.
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