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Register a new userOrder-out-of-disorder in a gas of elastic quantum strings in 2+1 dimensions
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J. Zaanen
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A limiting case of a dynamical stripe state which is of potential significance to cuprate superconductors is considered: a gas of elastic quantum strings in 2+1 dimensions, interacting merely via a hard-core condition. It is demonstrated that this gas solidifies always, by a mechanism which is the quantum analogue of the entropic interactions known from soft condensed matter physics.
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The finite temperature physics of the gas of elastic quantum strings as introduced in J. Zaanen, Phys. Rev. Lett. 84, 753 is investigated. This model is inspired on the stripes in the high Tc superconductors. We analyze in detail how the kinetic interactions of the zero temperature quantum problem crossover into the entropic interactions of the high temperature limit.
The competition between proximate electronic phases produces a complex phenomenology in strongly correlated systems. In particular, fluctuations associated with periodic charge or spin modulations, known as density waves, may lead to exotic superconductivity in several correlated materials. However, density waves have been difficult to isolate in the presence of chemical disorder, and the suspected causal link between competing density wave orders and high temperature superconductivity is not understood. Here we use scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge density wave (CDW) smoothly interfacing with the familiar tri-directional (triangular) CDW on the surface of the stoichiometric superconductor NbSe$_2$. Our low temperature measurements rule out thermal fluctuations, and point to local strain as the tuning parameter for this quantum phase transition. We use this discovery to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe$_2$. Our results highlight the importance of local strain in governing phase transitions and competing phenomena, and suggest a new direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials.
We study chiral phase transition and confinement of matter fields in (2+1)-dimensional U(1) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, $r=0$, defines a quantum critical point between the Higgs phase and the Coulomb phase. We consider only the critical point $r=0$ and the Coulomb phase with $r > 0$. The Dirac fermion acquires a dynamical mass when its flavor is less than certain critical value $N_{f}^{c}$, which depends quantitatively on the flavor $N_{b}$ and the scalar boson mass $r$. When $N_{f} < N_{f}^{c}$, the matter fields carrying internal gauge charge are all confined if $r eq 0$ but are deconfined at the quantum critical point $r = 0$. The system has distinct low-energy elementary excitations at the critical point $r=0$ and in the Coulomb phase with $r eq 0$. We calculate the specific heat and susceptibility of the system at $r=0$ and $r eq 0$, which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.
The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O(3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Neel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.
We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons (stress photons), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson-Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this deconfined mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a non-trivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.
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