Renormalization group analysis of competition between distinct order parameters
arXiv:1412.6252 · doi:10.1103/PhysRevD.90.125015
Abstract
We perform a detailed renormalization group analysis to study a (2+1)-dimensional quantum field theory that is composed of two interacting scalar bosons, which represent the order parameters for two continuous phase transitions. This sort of field theory can describe the competition and coexistence between distinct long-range orders, and therefore plays a vital role in statistical physics and condensed matter physics. We first derive and solve the renormalization group equations of all the relevant physical parameters, and then show that the system does not have any stable fixed point in the lowest energy limit. Interestingly, this conclusion holds in both the ordered and disordered phases, and also at the quantum critical point. Therefore, the originally continuous transitions are unavoidably turned to first-order due to ordering competition. Moreover, we examine the impacts of massless Goldstone boson generated by continuous symmetry breaking on ordering competition, and briefly discuss the physical implications of our results.
arXiv comment13 pages, 16 figures
References in corpus (28)
- Exact evolution equation for the effective potential
- Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
- How to detect fluctuating order in the high-temperature superconductors
- Renormalization Group Approach to Interacting Fermions
- Spinor Bose-Einstein condensates
- Quantum phase transitions
- Functional renormalization group approach to correlated fermion systems
- Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
- d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
- Quantum Criticality: competing ground states in low dimensions
- Quantum Criticality
- Superconducting Vortex with Antiferromagnetic Core
- Spin ordering quantum transitions of superconductors in a magnetic field
- Competing order and nature of the pairing state in the iron pnictides
- Theory of Ferromagnetic Superconductivity
- Nematicity as a probe of superconducting pairing in iron-based superconductors
- Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
- A Model for Superconductivity in Ferromagnetic ZrZn2
- Competing order in correlated electron systems made simple: Consistent fusion of functional renormalization and mean-field theory
- Stability of Quantum Critical Points in the Presence of Competing Orders
- Singularity of the London penetration depth at quantum critical points in superconductors
- How many quantum phase transitions exist inside the superconducting dome of the iron pnictides?
- Spin waves in a Bose Ferromagnet
- Suppression of superconductivity at nematic critical point in underdoped cuprates
- Nematic order in the vicinity of a vortex in superconducting FeSe
- Charged fixed point in the Ginzburg-Landau superconductor and the role of the Ginzburg parameter
- Phenomenological theory of spinor Bose-Einstein condensates
- Competition between superconductivity and nematic order in high- superconductor
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