Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDeconfined quantum critical point in one dimension
104
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice $S=1/2$ $J$-$Q$ model. The critical correlation function of the $Q$ terms gives a scaling dimension corresponding to the value $ u = 0.455 pm 0.002$ of the correlation-length exponent. This value agrees with previous (less precise) results from conventional methods, e.g., finite-size scaling of the near-critical order parameters. We also study the $Q$-derivatives of the Binder cumulants of the order parameters for $L^2$ lattices with $L$ up to $448$. The slope grows as $L^{1/ u}$ with a value of $ u$ consistent with the scaling dimension of the $Q$ term. There are no indications of runaway flow to a first-order phase transition. The mutually consistent estimates of $ u$ provide compelling support for a continuous deconfined quantum-critical point.
In this paper we discuss the N$acute{e}$el and Kekul$acute{e}$ valence bond solids quantum criticality in graphene Dirac semimetal. Considering the quartic four-fermion interaction $g(bar{psi}_iGamma_{ij}psi_j)^2$ that contains spin,valley, and sublattice degrees of freedom in the continuum field theory, we find the microscopic symmetry is spontaneously broken when the coupling $g$ is greater than a critical value $g_c$. The symmetry breaking gaps out the fermion and leads to semimetal-insulator transition. All possible quartic fermion-bilinear interactions give rise to the uniform critical coupling, which exhibits the multicritical point for various orders and the Landau-forbidden quantum critical point. We also investigate the typical critical point between N$acute{e}$el and Kekul$acute{e}$ valence bond solid transition when the symmetry is broken. The quantum criticality is captured by the Wess-Zumino-Witten term and there exist a mutual-duality for N$acute{e}$el-Kekul$acute{e}$ VBS order. We show the emergent spinon in the N$acute{e}$el-Kekul$acute{e}$ VBS transition , from which we conclude the phase transition is a deconfined quantum critical point. Additionally, the connection between the index theorem and zero energy mode bounded by the topological defect in the Kekul$acute{e}$ VBS phase is studied to reveal the N$acute{e}$el-Kekul$acute{e}$ VBS duality.
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 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 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 deconfined quantum critical point from the concept of quantum information.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
