Variational quantum simulation of the quantum critical regime

The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures. While it is of great physical interest, simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity. In this paper, we propose a variational approach, which minimizes the variational free energy, to simulate and locate the quantum critical regime on a quantum computer. The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state, in which the entropy can be analytically obtained from the initial state, and thus the free energy can be accessed conveniently. With numeral simulation, we show, using the one-dimensional Kitaev model as a demonstration, the quantum critical regime can be identified by accurately evaluating the temperature crossover line. Moreover, the dependence of both the correlation length and the phase coherence time with the temperature are evaluated for the thermal states. Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits

Cho-Maison Monopole-antimonopole Pair in Standard Model

We present numerical solutions corresponding to a pair of Cho-Maison monopole and antimonopole (MAP) in the SU(2)$\times$U(1) Weinberg-Salam (WS) theory, which possess magnetic charge $\pm 4\pi/e$. The system was investigated at physical Weinberg angle, $\tan\theta_W=0.53557042$, while the Higgs self-coupling constant, $0\leq\beta\leq1.7704$ and at physical $\beta=0.77818833$, while $0.4675\leq\tan\theta_W\leq10$. Numerical data was compared with MAP solutions found in the SU(2) Yang-Mills-Higgs (YMH) theory. Magnetic dipole moment ($\mu_m$), pole separation ($d_z$) and Higgs modulus at the origin ($z_0$) of the numerical solutions are calculated and analyzed. A major difference exists between these two types of MAP, where for Cho-Maison MAP, there exists an upper bound ($\beta=1.7704$) after which no solution can be found, a feature not present in the SU(2) MAP configuration

System of excited monopole-antimonopole pair in the Weinberg-Salam model

We investigate further the properties of axially symmetric monopole-antimonopole pair in the standard Weinberg-Salam model. By using a novel data sampling approach, we have obtained and analyzed 300 numerical solutions corresponding to physical Higgs self-coupling $\beta=0.7782$ and the Weinberg angle $\tan\theta_W=0.5358$. We calculate the energy of these solutions and confirm that they reside in a range of 13.1690 - 21.0221 TeV. In addition, a unique pattern is shown when the data are arranged according to an algorithm based on the system's symmetry, which seems to indicate the system is oscillating. We also calculate numerically the magnetic charge of the solutions and confirm that their values are indeed $\pm\frac{4\pi}{e}\sin^2\theta_W$.Comment: arXiv admin note: text overlap with arXiv:2107.0488

Evaluating Mechanical Properties of Environmentally Friendly Leather Substitute (Eco-Leather)

Leather and pleather (plastic leather, mainly polyurethane and polyvinyl chloride PVC) are widely used materials in apparel and footwear products. According to the American Apparel and Footwear Association (AAFA, 2009), in 2008, the US consumption of footwear was 2.2 billion pairs, among which about one third were categorized as leather products and one third as plastic/vinyl products. The chemical processes to convert raw animal hides to leather, especially tanning, cause environmental pollution and human health problems. Chromium salts are used in about 90% of global tanning production (Nair et al., 2012)

Dyonic Half-Monopole in Weinberg-Salam Theory

We construct and study numerical solutions corresponding to electrically charged half-monopole in Weinberg-Salam theory. These solutions possess magnetic charge $q_m = 2 n \pi/e$ and electric charge $q_{e}$ that depends on the electric charge parameter $\eta$, as well as net zero neutral charge. The energies for these half-dyons are finite and calculated to be in the range of 4.7314 - 18.3888 TeV. We also explore a two-half-monopole system which carries magnetic charge $4 \pi /e$ and compare its properties with the Cho-Maison monopole.Comment: 12 pages, 7 figure

Gravitating Cho-Maison Monopole

We study numerical solutions corresponding to spherically symmetric gravitating electroweak monopole and magnetically charged black holes of the Einstein-Weinberg-Salam theory. The gravitating electroweak monopole solutions are quite identical to the gravitating monopole solution in SU(2) Einsten-Yang-Mills-Higgs theory, but with distinctive characteristics. We also found solutions representing radially excited monopole, which has no counterpart in flat space. Both of these solutions exist up to a maximal gravitational coupling before they cease to exist. Lastly we also report on magnetically charged non-Abelian black holes solutions that is closely related to the regular monopole solutions, which represents counterexample to the `no-hair' conjecture.Comment: 10 pages, 7 figure