Using the example of two-dimensional (2D) Ising model, we show that in contrast to what can be done configuration space, tensor renormalization group (TRG) formulation allows one write exact, compact, and manifestly local blocking formulas exact coarse grained expressions for partition function. We argue similar results should hold most models studied by lattice gauge theorists. provide several 2D spin (the O(2) O(3) sigma SU(2) principal chiral model) 3D theories with groups Z_2, U(1)...

Using the tensor renormalization group method based on higher-order singular value decomposition, we have studied thermodynamic properties of continuous $XY$ model square lattice. The temperature dependence free energy, internal and specific heat agree with Monte Carlo calculations. From field magnetic susceptibility, find Kosterlitz-Thouless transition to be $0.8921(19)$, consistent as well high series expansion results. At temperature, critical exponent $\ensuremath{\delta}$ is estimated...

We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E 83, 056703 (2011)] to study spin-1/2 frustrated Heisenberg ${J}_{1}$-${J}_{2}$ model on an $L\ifmmode\times\else\texttimes\fi{}L$ square lattice with $L$ $=$ 8, 16, and 32. By treating elements as variational parameters, we obtain ground for different ${J}_{2}/{J}_{1}$ values, investigate staggered magnetizations, nearest-neighbor spin-spin correlations, order parameters. In addition well-known N\'eel...

We consider the sign problem for classical spin models at complex $\ensuremath{\beta}=1/{g}_{0}^{2}$ on $L\ifmmode\times\else\texttimes\fi{}L$ lattices. show that tensor renormalization group method allows reliable calculations larger Im$\ensuremath{\beta}$ than reweighting Monte Carlo method. For Ising model with $\ensuremath{\beta}$ we compare our results exact Onsager-Kaufman solution finite volume. The Fisher zeros can be determined precisely check convergence of $O(2)$ lattices when...

Tensor networks are used to represent the wave functions of quantum many-body systems, but standard approaches only consider two-body entanglement and do not work well for ``frustrated'' where underlying lattice geometry makes three- or also important. A new tensor-network approach based on a novel tensor concept describing such ``simplex'' shows great promise.

It has been known that a charged polaron will reach constant speed after being accelerated only for short time in an electric field. Within dynamical nonadiabatic evolution method, we simulate the motion of under influence field which is present different periods. We find lattice oscillation behind be localized and separated with moving once turned off. shown nothing but breather, specifically, multibreather excitation. Furthermore, it breather bears incresed energy due to acting on polaron,...

Hydrogen gas produced by electrolysis has been considered as an excellent alternative to fossil fuels. Developing non-noble metal catalysts with high electrocatalytic activities is effective way reduce the cost of hydrogen production. Recently, black phosphorus (BP) based materials have reported good potential electrocatalysts for evolution reaction (HER). Herein, we systematically study catalytic performance monolayer BP (phosphorene) and several chemically modified phosphorenes (N/S/C/O...

Using the tensor renormalization group method based on higher-order singular value decomposition,we have studied phase transitions of five-state clock model square lattice.The temperature dependence specific heat indicates system has two transitions, as verified clearly in correlation function. By investigating magnetic susceptibility, we can only obtain upper critical Tc2 = 0.9565(7). From fixed-point tensor, locate transition temperatures at Tc1 0.9029(1) and 0.9520(1), consistent with MC...

In the context of tensor network states, we for first time reformulate corner transfer matrix renormalization group (CTMRG) method into a variational bilevel optimization algorithm. The solution problem corresponds to fixed-point environment pursued in conventional CTMRG method, from which partition function classical statistical model, represented by an infinite network, can be efficiently evaluated. validity this idea is demonstrated high-precision calculation residual entropy dimer and...

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, which some degrees freedom remain disordered. This situation may arise from frustration interactions, but also irregular unfrustrated lattice structure. We study partial long-range order a range antiferromagnetic $q$-state models on different two-dimensional lattices and for all relevant values $q$. exploit...

With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy $G(T,h)$, to study phase transitions in classical spin lattice models. A cross derivative, i.e., second-order partial derivative of $G(T,h)$ with respect both temperature and is calculated precisely locate critical temperature, which also reveals nature a transition. The strategy efficient universal, as exemplified by five-state clock model, two-dimensional (2D) 3D Ising...

We show that the Tensor Renormalization Group (TRG) method can be applied to O(N) spin models, principal chiral models and pure gauge theories (Z2, U(1) SU(2)) on (hyper) cubic lattices. explain contrarily some common belief, it is very difficult write compact formulas expressing blockspinning of lattice models. in contrast other approaches, TRG formulation allows us exact blocking with numerically controllable truncations. The basic reason separates neatly degrees freedom inside block which...

In order to clarify the coexistence of a Fermi edge and steplike multiphonon structure, recently observed in photoemission spectra (PES) boron-doped diamond, we apply path-integral theory calculate PES, using many-impurity Holstein model simple cubic lattice. Being lightly doped by boron as an acceptor, diamond shows $p$-type character with activation energy gap about $0.37\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. We find that, due electron-phonon coupling increase dopant concentration,...

A new path-integral theory is developed to calculate the photoemission spectra (PES) of correlated many-electron systems. The application study on Bi2Sr2CaCu2O8 (Bi2212) and boron-doped diamond (BDD) discussed in details. It found that isotopic shift angle-resolved Bi2212 due off-diagonal quadratic electron-phonon (e-ph) coupling, whereas presence electron-electron repulsion partially suppresses this effect. For BDD, a semiconductor-metal phase transition, which induced by increasing e-ph...