Emergent Symmetry and Dimensional Reduction at a Quantum Critical Point

Abstract

We show that the spatial dimensionality of the quantum critical point associated with Bose--Einstein condensation at T=0 is reduced when the underlying lattice comprises a set of layers coupled by a frustrating interaction. For this purpose, we use an heuristic mean field approach that is complemented and justified by a more rigorous renormalization group analysis. Due to the presence of an emergent symmetry, i.e. a symmetry of the ground state that is absent in the underlying Hamiltonian, a three--dimensional interacting Bose system undergoes a chemical potential tuned quantum phase transition that is strictly two dimensional. Our theoretical predictions for the critical temperature as a function of the chemical potential correspond very well with recent measurements in BaCuSi${}_2$O${}_6$.

References in corpus (16)

• Locally critical quantum phase transitions in strongly correlated metals
• Coupled Ladders in a Magnetic Field
• Magnetic Field-Induced Condensation of Triplons in Han Purple Pigment BaCuSi${}_2$O${}_6$
• Dimensional reduction at a quantum critical point
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• Algebraic Approach to Interacting Quantum Systems
• Generalized Elitzur's Theorem and Dimensional Reduction
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• Role of anisotropy in the spin-dimer compound BaCuSi2O6
• Low temperature structural phase transition and incommensurate lattice modulation in the spin gap compound BaCuSi2O6
• Quantum phase transitions and dimensional reduction in antiferromagnets with inter-layer frustration
• Reduced dimensionality in layered quantum dimer magnets: Frustration vs. inhomogeneous condensates
• Can Frustration Preserve a Quasi-Two-Dimensional Spin Fluid?

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• Ordered magnetic phases of the frustrated spin-dimer compound Ba3Mn2O8
• Magnetic frustration in BaCuSi2O6 released
• Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence
• Dimensional crossover in the quasi-two-dimensional Ising-O(3) model
• Theory of the field-induced BEC in the frustrated spin-1/2 dimer compound BaCuSi2O6
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Dynamical Particle Hole Asymmetry in Cuprate Superconductors
• Emergent SU(3) symmetry in random spin-1 chains
• Spatially Resolved Magnetization in the Bose-Einstein Condensed State of BaCuSi2O6: Evidence for Imperfect Frustration
• Two types of adjacent dimer layers in the low temperature phase of BaCuSi2O6
• Multiple Magnetic Bilayers and Unconventional Criticality without Frustration in BaCuSi${}_2$O${}_6$
• Theory of Magnetic Field-Induced Bose-Einstein Condensation of Triplons in Ba3Cr2O8
• Dimensional reduction by geometrical frustration in a cubic antiferromagnet composed of tetrahedral clusters
• Highly-symmetric random one-dimensional spin models
• Magnon Condensation in Dimerized Antiferromagnets with Spin-Orbit Coupling
• Crossover Behavior from Decoupled Criticality
• Finite-Temperature Transition in the Spin-Dimer Antiferromagnet BaCuSi2O6
• Crystal growth with oxygen partial pressure of the $BaCuS{i}_2{O}_6$ and $B{a}_{1-x}S{r}_{x}CuS{i}_2{O}_6$ spin dimer compounds
• Emergent SU(N) symmetry in disordered SO(N) spin chains
• Dimensional reduction of Kitaev spin liquid at quantum criticality
• Emergent critical phenomenon in spin-1/2 ferromagnetic-leg ladders: Quasi-one-dimensional Bose--Einstein condensate
• Investigating field-induced magnetic order in Han Purple by neutron scattering up to 25.9 T
• Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?