Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the $J_{1x}$-$J_{1y}$-$J_2$ model, which contains anisotropic nearest-neighbor couplings $J_{1x}$, $J_{1y}$ and the next nearest neighbor coupling $J_2$. For small $J_{1y}/J_{1x}$, by tuning $J_2$, a direct continuous transition between the AFM and valence bond solid phase is observed.(Of course, the possibility of weakly first order transition can not be fully excluded.) With growing $J_{1y}/J_{1x}$, a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM--VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL--VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.Comment: 5+7 pages, 4+11 figure

Tensor network study of the spin-1/2 square-lattice J1J_1-J2J_2-J3J_3 model: incommensurate spiral order, mixed valence-bond solids, and multicritical points

We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS.Comment: 13 pages; 17 figure

Synthetic cell lines for recombinant AAV production

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Synthetic cell lines for recombinant AAV production

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4-(4-Nitro­benzene­sulfonamido)pyridinium trichloro­acetate

In the crystal structure of the title compound, C11H10N3O4S·C2Cl3O2, the dihedral angle between the two six-membered rings is 69.2 (1)°. The mol­ecules are connected via inter­molecular N—H⋯O hydrogen bonding

Gapless quantum spin liquid and global phase diagram of the spin-1/2 J1J_1-J2J_2 square antiferromagnetic Heisenberg model

The nature of the zero-temperature phase diagram of the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on a square lattice has been debated in the past three decades, which may hold the key to understand high temperature superconductivity. By using the state-of-the-art tensor network method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram the $J_1$-$J_2$ Heisenberg model up to $24\times 24$ sites, we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region $0.56\lesssim J_2/J_1\leq0.61$ before the system enters the well known collinear antiferromagnetic phase. The physical nature of the discovered gapless QSL and potential experimental implications are also addressed. We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group (DMRG) method through one-to-one direct benchmark for small system sizes, and thus give rise to a very solid PEPS calculation beyond DMRG. Our numerical evidences explicitly demonstrate the huge power of PEPS for precisely capturing long-range physcis for highly frustrated systems, and also demonstrate the finite PEPS method is a very powerful approach to study strongly corrleated quantum many-body problems