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arXiv:1906.03850 · Physical review. B./Physical review. B

Fidelity as a probe for a deconfined quantum critical point

Gaoyong Sun, Bo-Bo Wei, Su-Peng Kou

Published Aug 28, 2019• 31 citations
arXivHTMLPDF

Abstract

The deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken-symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly-first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study the deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density-matrix renormalization-group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the idea that the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size-scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at the deconfined quantum critical point from the concept of quantum information.

DOI
10.1103/physrevb.100.064427

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The deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken-symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly-first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study the deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density-matrix renormalization-group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the idea that the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size-scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at the deconfined quantum critical point from the concept of quantum information.
We investigate the ground-state quantum entanglement in a one-dimensional incarnation of deconfined quantum critical point by making use of the finite-size density matrix renormalization group method. We observe two distinct behaviors of two-site entanglement calculated on odd and even bonds, and the difference O_{E} is shown to obey conventional scaling relations for order parameters. Accurate deconfined critical point and associated critical exponents are numerically extracted from finite-size scaling analyses. We further notice a close similarity between O_{E} and the valence-bond-solid order parameter and same observations are also obtained for quantum coherence and trace distance. Furthermore, the deconfined critical point is suggested to possess rich quantum entanglement other than the two-site entanglement from the residual entanglement perspective. Our work explores the critical characteristics of the one-dimensional deconfined quantum critical point from the quantum information aspect and provides insights for its ground-state entanglement structure.
The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite-size analysis applied to the so-obtained numerical results confirms the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy's second derivative, which can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined.
A deconfined quantum critical point (DQCP) is a continuous transition between ordered phases with unrelated broken symmetries, beyond the Landau-Ginzburg-Wilson paradigm. In one dimension, such a transition between a zzz-polarized ferromagnet (zFM) and a valence-bond solid (VBS) is well established numerically in a frustrated spin-1/21/21/2 chain. Here we ask whether a superconducting quantum processor can resolve this transition and its signatures despite finite-size effects and device noise. The ground states are prepared by ancilla-projected quantum imaginary-time evolution (QITE), whose exact target states are compressed by tensor-network optimization into shallow depth quantum circuits. The hardware data distinguish the phases through their order parameters, spin and dimer correlations, structure factors, correlation ratios, and snapshot distributions. The crossing of the order parameters locates the transition, and its finite-size extrapolation lies close to the thermodynamic-limit value obtained from large-scale numerics. A noise model based on the device calibration accounts quantitatively for the reduced amplitudes measured on hardware. Our findings demonstrate that a Landau-forbidden transition between competing orders can be resolved on current quantum processors.
By means of the density matrix renormalization group technique, the scaling relation of the fidelity susceptibility proposed recently is verified for the spin-one XXZXXZXXZ spin chain with an on-site anisotropic term. Moreover, from the results of both the fidelity susceptibility and the entanglement entropy, the critical points and some of the corresponding critical exponents are determined through a proper finite-size scaling analysis, and these values agree with the findings in the literature. Thus our work provides a numerical support of the use of the fidelity in detecting quantum phase transitions.
We study the fidelity susceptibility of a quantum antiferromagnetic Ising chain with a long-range power-law interaction $1/{r}^{\ensuremath{\alpha}}$ using the large-scale density matrix renormalization group method. We find that the critical adiabatic dimension $\ensuremath{\mu}=2$ and the critical exponent of the correlation length $\ensuremath{\nu}=1$ for arbitrary $\ensuremath{\alpha}>0$, indicating all quantum phase transitions are second-order Ising transitions. In addition, we numerically determine the complete phase diagram for $0<\ensuremath{\alpha}\ensuremath{\le}3$ from the data collapse of the fidelity susceptibility and show that the critical point hc{h}_{c}hc​ changes monotonously with respect to $\ensuremath{\alpha}$. This work will shed light on the nature of phase transitions in the quantum long-range antiferromagnetic Ising chain from a quantum information perspective.
We perform a numerical study of a spin-1/2 model with ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ 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 the Landau-Ginzburg-Wilson symmetry-breaking theory.