The possible connection between High-T$_c$ superconductivity and quantum chromodynamics is considered that is based on two interacting Ginzburg-Landau equations. For High-T$_c$ superconductivity these two equations describe Cooper electrons interacting with different kind of quasi particles (phonons, magnons, excitons and so on). The interaction term describes a possible interaction between different kind of quasi particles. For quantum chromodynamics the equations describe two kinds of gauge condensates. The condensates describe a gauge potential from a subalgebra of the SU(3) gauge group and the corresponding coset. Regular solutions are found which describe the situation where one field, $ψ_1$, is pushed out by another, $ψ_2$.
We study superconductivity in the hadron-quark mixed phase of planar quantum chromodynamics (QCD) within the large $N$ limit of a Gross-Neveu model modified by a repulsive vector term. At high densities, the combination of scalar attraction and repulsive space-like part of the vector interaction squeezes quarks into baryonic composite states, i.e., Dirac fermions with even numbers of bosonic vortices attached. The time-like vector component induces Cooper pairing between these Fermi surface modes. Remarkably, at zero temperature, competition between the quark density and mass destroys supercon…
Using the standard Hamiltonian of the BCS theory, we show that in an ensemble of interacting fermions there exists a coherent state $|NC>$, which nullifies the Hamiltonian of the interparticle interaction. This state has an analogy with the well-known in quantum optics coherent population trapping effect (CPT). A possible application of such CPT-like states in the superconductivity theory is discussed.
Non-interacting particles obeying certain fractional statistics have been predicted to exhibit superconductivity. We discuss the issue in an attractively interacting system of spinful semions on a lattice by numerically investigating the presence of off-diagonal long-range order at zero temperature. For this purpose, we construct a Hubbard model wherein two semions with opposite spin can virtually coincide while maintaining consistency with the fractional braiding statistics. Clear off-diagonal long range order is seen in the strong coupling limit, consistent with the expectation that a pair o…
MgB$(p^{n_σ}p^{n_π})_{2}$ is classified as a system with strongly interacting $σ$-electrons and non-correlated $π$-electrons of boron ions. The kinematic and Coulomb interaction V between the orbitally degenerated $σ$-electrons provide the superconducting state with an anisotropic gap of s*-wave symmetry. The critical temperature $T_c$ has a non-monotonic dependence on the distance r between the centers of gravity of $σ$- and $π$-bands. MgB$_2$ corresponds to r=0.085 eV and V=0.45 eV in our model with flat bands. The derived superconducting density of electronic states is in good agreement wit…
Low-temperature thermodynamic properties of strongly interacting Fermi liquids with fermion condensate are investigated. We demonstrate that the spin susceptibility of these systems exhibits the Curie-Weiss law, and the entropy contains a temperature-independent term. The excessive entropy is released at the superconducting transition, enhancing the specific heat jump Delta C and rendering it proportional to the effective Curie constant. The theoretical results are favorably compared with the experimental data on the heavy fermion metal CeCoIn5, as well as He-3 films.
To explore whether a flat-band system can accommodate superconductivity, we consider repulsively interacting fermions on the diamond chain, a simplest quasi-one-dimensional system that contains a flat band. Exact diagonalization and the density-matrix renormalization group (DMRG) are used to show that we have a significant binding energy of a Cooper pair with a long-tailed pair-pair correlation in real space when the total band filling is slightly below $1/3$, where the dispersive band interacts with the flat band that is empty but close to $E_F$. Pairs selectively formed across the outer site…
We investigate the 1/N expansion proposed recently as a strategy to include quantum fluctuation effects in the nonrelativistic, attractive Fermi gas at and near unitarity. We extend the previous results by calculating the next-to-leading order corrections to the critical temperature along the whole BCS-BEC crossover. We demonstrate explicitly that the extrapolation from the mean-field approximation, based on the $1/N$ expansion, provides a useful approximation scheme only on the BCS side of the crossover. We then apply the technique to the study of strongly interacting relativistic many-fermio…
Motivated by recent experiments realizing correlated phenomena and superconductivity in 2D van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model, and a partially flat band structure containing a non-dispersing region, with identical total non-interacting bandwidth $W$. For both repulsive and attractive weak interactions …
What distinguishes trivial from topological superluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting variation of the Kitaev model, the Richardson-Gaudin-Kitaev chain, that remains exactly solvable for periodic and antiperiodic boundary conditions. Our model allows us to identify fermionic parity switches that distinctively characterize topological superconductivity in interacting many-body systems. Although the Majorana zero-modes in this model have only a power-l…
Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the non-interacting) Hamiltonian. We describe such a renormalized perturbation expansion for interacting Fermi systems, which treats Fermi surface shifts and superconductivity with an arbitrary gap function via additive counterterms. The expansion is formulated explicitly for the Hubbard model to second order in the interaction. Numerical soutions of the self-consistency condition determining the Fermi surface and the gap functio…
High-temperature charge-4e superconductivity in SU(4) interacting fermions
Beijing National Laboratory for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；New Cornerstone Science Laboratory, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所新基石科学实验室）
It is assumed that in some sense the High-T$_c$ superconductivity is similar to the quantum chromodynamics (QCD). This means that the phonons in High-T$_c$ superconductor have the strong interaction between themselves like to gluons in the QCD. At the experimental level this means that in High-T$_c$ superconductor exists the nonlinear sound waves. It is possible that the existence of the strong phonon-phonon interaction leads to the confinement of phonons into a phonon tube (PT) stretched between two Cooper electrons like a hypothesized flux tube between quark and antiquark in the QCD. The flu…
We study the physical property of pair density wave (PDW) and fluctuating PDW, and use it to build an effective theory of the strongly interacting pseudogap phase in cuprate high temperature superconductors. In Chapter2, we study how Fulde-Ferrell state, the simplest form of PDW, responds to incident light. The collective motion of the condensate plays a key role; gauge invariance guides us to the correct result. From Chapter 3 to Chapter 7, we construct a pseudogap metallic state by considering quantum fluctuating PDW. We analyze a recent scanning tunneling microscope (STM) discovery of perio…
At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of strongly nonlinear field can form a non-associative algebra. It is shown that such algebra can be described as an algebra of some pairs. The comparison of presented techniques with the Green's functions method in the superconductivity theory is made. A possible application to the QCD and High-T$_c$ superconductivity theory is discussed.
We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in an homogeneous p + ip superconducting (SC) phase at high or low electron densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain p-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above Tsc, generating a…
When interacting electrons are confined to low-dimensions, the electron-electron correlation effect is enhanced dramatically, which often drives the system into exhibiting behaviors that are otherwise highly improbable. Superconductivity with the strongest electron correlations is achieved in heavy-fermion compounds, which contain a dense lattice of localized magnetic moments interacting with a sea of conduction electrons to form a 3D Kondo lattice. It had remained an unanswered question whether superconductivity would persist upon effectively reducing the dimensionality of these materials fro…
In this paper, we investigate the disordered attractive Hubbard model by combining dynamical mean field theory, coherent potential approximation and iterated perturbation theory for superconductivity as an impurity solver. Disorder is introduced in the local attraction $U$. We assume that $U$ is distributed according to a bimodal probability distribution, wherein an $x$ fraction of sites are pairing centers ($U\neq0$) and $(1-x)$ fraction of sites are non-interacting ($U=0$). It is found that beyond a critical $x=x_c$, a first order metal-superconductor phase transition leads to superconductiv…
In a flat band superconductor, bosonic excitations can disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all space groups. We analytically compute their many-body excitations and find that the Cooper pair bound states and density excitations obey an effective single-particle Hamiltonian written in terms of the non-interacting wavefunctions. These bound states possess a unique zero-energy excitation whose quadratic dispersion is determined by the minimal quantum me…
Superconductivity is a quantum phenomena arising, in its simplest form, from pairing of fermions with opposite spin into a state with zero net momentum. Whether superconductivity can occur in fermionic systems with unequal number of two species distinguished by spin, atomic hyperfine states, flavor, presents an important open question in condensed matter, cold atoms, and quantum chromodynamics, physics. In the former case the imbalance between spin-up and spin-down electrons forming the Cooper pairs is indyced by the magnetic field. Nearly fifty years ago Fulde, Ferrell, Larkin and Ovchinnikov…
We study theoretically the two interacting one-dimensional helical modes at the edges of the quantum spin Hall systems. A new type of inter-edge correlated liquid (IECL) without the spin gap is found. This liquid shows the diverging density wave (DW) and superconductivity (SC) correlations much stronger than those of the spinfull electrons. Possible experimental observations are also discussed.
We study s-wave superconductivity in the two-dimensional square lattice attractive Hubbard Hamiltonian for various inhomogeneous patterns of interacting sites. Using the Bogoliubov-de Gennes (BdG) mean field approximation, we obtain the phase diagram for inhomogeneous patterns in which the on-site attractive interaction U_i between the electrons takes on two values, U_i=0 and -U/(1-f) (with f the concentration of non-interacting sites) as a function of average electron occupation per site n, and study the evolution of the phase diagram as f varies. In certain regions of the phase diagram, inho…
It is demonstrated that the transition temperature (Tc) of high-Tc superconductors is determined by their layered crystal structure, bond lengths, valency properties of the ions, and Coulomb coupling between electronic bands in adjacent, spatially separated layers. Analysis of 31 high-Tc materials (cuprates, ruthenates, rutheno-cuprates, iron pnictides, organics) yields the universal relationship for optimal compounds, kBTc0 = β/\ellζ, where \ell is related to the mean spacing between interacting charges in the layers, ζ is the distance between interacting electronic layers, β is a universal c…
Switching on interchain coupling in a system of one-dimensional strongly interacting chains often leads to an ordered state. Quite generally, there is a competition between an insulating charge-density-wave and a superconducting state. In the case of repulsive interactions, charge-density wave usually wins over superconductivity. Here, we show that a suitable modulation in the form of a period 4 bond-centered stripe can reverse this balance even in the repulsive case and produce a superconducting state with relatively high temperature.
Monolayer transition metal dichalcogenides (TMDs) host deeply bound excitons interacting with itinerant electrons, and as such they represent an exciting new quantum many-body Bose-Fermi mixture. Here, we demonstrate that electrons interacting with a Bose-Einstein condensate (BEC) of exciton-polaritons can realise a two-dimensional topological $p_x+ip_y$ superconductor. Using strong coupling Eliashberg theory, we show that this is caused by an attractive interaction mediated by the BEC, which overcompensates the repulsive Coulomb interaction between the electrons. The hybrid light-matter natur…
We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.
The superconducting transition temperatures of high-Tc compounds based on copper, iron, ruthenium and certain organic molecules are discovered to be dependent on bond lengths, ionic valences, and Coulomb coupling between electronic bands in adjacent, spatially separated layers [1]. Optimal transition temperature, denoted as T_c0, is given by the universal expression $k_BT_c0 = e^2 Λ/ \ellζ$; $\ell$ is the spacing between interacting charges within the layers, ζis the distance between interacting layers and Λis a universal constant, equal to about twice the reduced electron Compton wavelength (…
We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the hetero-structures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity {\it without breaking time-reversal symmetry} is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the inter-layer interaction is repu…
We propose the model of a manifold of one-dimensional interacting electron systems to account for the superconductivity observed in ropes of nanotubes. We rely on the strong suppression of single-particle hopping between neighboring nanotubes in a disordered rope and conclude that the tunnelling takes place in pairs of electrons, which are formed within each nanotube due to the existence of large superconducting correlations. Our estimate of the transition temperature is consistent with the values that have been measured experimentally in ropes with about 100 metallic nanotubes.
A key question in the theory of high-temperature superconductivity is whether Off-diagonal Long-Range Order (ODLRO) can be induced wholly or in large part by repulsive electronic correlations. Electron pairs on Cuprate and the iron-based pnictide and chalcogenide alternant lattices may interact with a strong short-range Coulomb repulsion and much weaker longer range attractive tail. Here we show that such interacting electrons can cooperate to produce a superconducting state in which time-reversed electron pairs effectively avoid the repulsive part but reside predominantly in the attractive re…
Unique among alkali-doped $\textit {A}$$_3$C$_{60}$ fullerene compounds, the A15 and fcc forms of Cs$_3$C$_{60}$ exhibit superconducting states varying under hydrostatic pressure with highest transition temperatures at $T_\textrm {C}$$^\textrm {meas}$ = 38.3 and 35.2 K, respectively. Herein it is argued that these two compounds under pressure represent the optimal materials of the $\textit {A}$$_3$C$_{60}$ family, and that the C$_{60}$-associated superconductivity is mediated through Coulombic interactions with charges on the alkalis. A derivation of the interlayer Coulombic pairing model of h…
Interacting Bose-Fermi systems play a central role in condensed matter physics. Here, we analyze a novel Bose-Fermi mixture formed by a cavity exciton-polariton condensate interacting with a two-dimensional electron system. We show that that previous predictions of superconductivity [F.P. Laussy, Phys. Rev. Lett. 10, 104 (2010)] and excitonic supersolid formation [I.A. Shelykh, Phys. Rev. Lett. 14, 105 (2010)] in this system are closely intertwined- resembling the predictions for strongly correlated electron systems such as high temperature superconductors. In stark contrast to a large majorit…
We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory: SpinSCDFT, by extending the Hohenberg-Kohn theorem and constructing the non-interacting Kohn- Sham system. An exchange-correlation functional for SpinSCDFT is derived from the Sham Schlüter connection between the SpinSCDFT Kohn-Sham and a self-energy in Eliashberg approximation. The reference Eliashberg equations for superconductors in the presence of magnetism are also derived and discussed.
We show that optically pumped semiconductors can exhibit superconductivity. We illustrate this phenomenon in the case of a two-band semiconductor tunnel-coupled to broad-band reservoirs and driven by a continuous wave laser. More realistically, we also show that superconductivity can be induced in a two-band semiconductor interacting with a broad-spectrum light source. We furthermore discuss the case of a three-band model in which the middle band replaces the broad-band reservoirs as the source of dissipation. In all three cases, we derive the simple conditions on the band structure, electron-…
The usual formulation of the BCS ansatz for superconductivity in the grand canonical ensemble makes the handling of the Pauli exclusion principle between paired electrons straightforward. It however tends to mask that many-body effects between Cooper pairs interacting through the reduced BCS potential are entirely controlled by this exclusion. To show it up, one has to work in the canonical ensemble. Pauli blocking between a fixed number of composite bosons is however known to be difficult to handle. To do it, we here develop a commutator formalism for Cooper pairs, along the line we used for …
We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution.
We develop a finite temperature mean field theory in the path integral picture for an extremely dilute system of interacting Fermions in a plane. In the limit of short ranged interactions, the system is shown to undergo a phase transition to a superconducting regime. Unlike the well known BCS transition for metals, this phase transition is found to be very sensitive to the two dimensional nature of the problem. A quantitative estimate of this sensitivity is carried out by repeating the analysis at non-zero thickness. The validity of the mean field results are also proved using renormalization …
We analyze the mathematical structure of equations for temperature Tc of the superconductivity transition in a gas of interacting Fermi particles or at the phonon-mediated pairing in a metal in case of non-adiabatic conditions, i. e., when the characteristic phonon frequency is comparable or larger than the Fermi energy . The integral equations for Tc are derived in the logarithmical approximation. The equations contain no divergent terms in the anti-adiabatic limit.
We study a generalization of the standard holographic p-wave superconductor featuring two interacting vector order parameters. Basing our argument on the symmetry and linear response properties of the model, we propose it as a holographic effective theory describing a strongly coupled ferromagnetic superconductor. We show that the two order parameters undergo concomitant condensations as a manifestation of an intrinsically interlaced electric/magnetic dynamics. Such intertwined dynamics is confirmed by the study of the transport properties. We characterize thoroughly the equilibrium and the li…
We propose possible high-temperature superconductivity (SC) with singlet $s^\pm$-wave pairing symmetry in the single-orbital Hubbard model on the square-octagon lattice with only nearest-neighbor hopping terms. Three different approaches are engaged to treat with the interacting model for different coupling strengths, which yield consistent result for the $s^\pm$ pairing symmetry. We propose octagraphene, i.e., a monolayer of carbon atoms arranged into this lattice, as a possible material realization of this model. Our variational Monte Carlo study for the material with realistic coupling stre…
We study the ground state of the doped Hubbard model on the honeycomb lattice in the small doping and strongly interacting region. The nature of the ground state by doping holes into the anti-ferromagnetic Mott insulating states on the honeycomb lattice remains a long-standing unsolved issue, even though tremendous efforts have been spent to investigate this challenging problem. An accurate determination of the ground state in this system is crucial to understand the interplay between the topology of Fermi surface and strong correlation effect. In this work, we employ two complementary, state-…
Conventional Hartree-Fock mean field theory is used, for the first time, to investigate the full two-dimensional t-J model. To date, all other nontrivial mean field approaches modify the Hamiltonian or violate the double occupancy constraint. Unlike conventional mean field theory, these methods do not give variational results for the t-J model. The mean field phase diagram of the t-J model predicts enhanced superconductivity at the crossover between an insulating phase at low doping and a metallic phase at moderate doping. This behavior is remarkably similar to that of high temperature superco…
We present measurements of the temperature and field dependencies of the magnetization M(T,H) of Nd(O0.89F0.11)FeAs at fields up to 33T, which show that superconductivity with the critical temperature Tc ~ 51K cannot coexist with antiferromagnetic ordering. Although M(T,H) at 55 < T < 140K exhibits a clear Curie-Weiss temperature dependence corresponding to the Neel temperature TN ~ 11-12K, the behavior of M(T,H) below Tc is only consistent with either paramagnetism of weakly interacting magnetic moments or a spin glass state. We suggest that the anomalous magnetic behavior of an unusual high-…
I propose that a dopant charge singlet bonding state may arise from the hybridization of molecular orbitals in a cluster containing 13 Cu atoms in the CuO2 plane of the superconducting cuprates. This singlet state forms a pre-formed pair with low binding energy that is spatially bounded and weakly interacting, and that can undergo Bose-Einstein condensation. I show that this model is able to account, in a quantitative and natural way, for many of the thermodynamic and electronic characteristics of the superconducting cuprates, including many of the key experimental ARPES, muSR and microwave re…
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time-reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi-temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s-wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature versus doping phase diagram, the unco…
Sulfur has recently been found to be a superconductor at high pressure. At ~93 GPa Tc is 10.1 K, and the sulfur is in a base-centered orthorhombic (b.c.o) structure. At ~160 GPa Tc is 17 K and sulfur is in a rhobohedral (b-Po) structure. The mechanism for superconductivity in sulfur is not known; in particular, a band-structure calculation does not find superconductivity in sulfur until 500 GPa. Following work by Anderson, in a 2D strongly interacting non-fermi liquid system with some degree of disorder at T=0, the only known conducting state is a superconductor. Following this idea it has bee…
We use the weak coupling renormalization group method to examine the interplay between charge-density-wave and s-wave superconducting orders in a quasi-one-dimensional model of electrons interacting with acoustic phonons. The relative stability of both types of order is mapped out at arbitrary nesting deviations and Debye phonon frequency $ω_D$. We singled out a power law increase of the superconducting $T_c\sim ω_D^{0.7}$ from a quantum critical point of charge-density-wave order triggered by nesting alterations. The results capture the key features shown by the proximity between the two type…
We consider fermions on a 2D lattice interacting repulsively on the same site and attractively on the nearest neighbor sites. The model is relevant, for instance, to study the competition between antiferromagnetism and superconductivity in a Kondo lattice. We first solve the two-body problem to show that in the dilute and strong coupling limit the s-wave Bose condensed state is always the ground state. We then consider the many-body problem and treat it at mean-field level by solving exactly the usual gap equation. This guarantees that the superconducting wave-function correctly vanishes when …
Pairing of fermions is ubiquitous in nature and it is responsible for a large variety of fascinating phenomena like superconductivity, superfluidity of $^3$He, the anomalous rotation of neutron stars, and the BEC-BCS crossover in strongly interacting Fermi gases. When confined to two dimensions, interacting many-body systems bear even more subtle effects, many of which lack understanding at a fundamental level. Most striking is the, yet unexplained, effect of high-temperature superconductivity in cuprates, which is intimately related to the two-dimensional geometry of the crystal structure. In…
Thin superconducting films form a unique platform for geometrically-confined, strongly-interacting electrons. They allow an inherent competition between disorder and superconductivity, which in turn enables the intriguing superconducting-to-insulator transition and believed to facilitate the comprehension of high-Tc superconductivity. Furthermore, understanding thin film superconductivity is technologically essential e.g. for photo-detectors, and quantum-computers. Consequently, the absence of an established universal relationships between critical temperature ($T_c$), film thickness ($d$) and…
Although their crystal structures are complex, all high temperature superconductors contain some crystal planes consisting of only Cu and O atoms in a square lattice. Superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substitution of a single impurity atom at a Cu site creates a simple but powerful perturbation to these interactions. Detailed knowledge of the effects of such an impurity atom on the superconducting order parameter and on the quasi-particle local density of states (LDOS) could allow competing theories of high temperature supercon…
We show that two phenomena of superfluidity, superfluidity of weakly interacting bosons and superconductivity of the BCS model, are unified using the collective mode arising from the Berry connection for many-body wave functions. The superfluidity is attributed to the presence of this mode, which is stabilized by the interaction between particles that causes fluctuations of the number of particles participating in it. It is suggested that the existence of this collective mode and its stabilization is more fundamental to the occurrence of superconductivity than the electron-pair formation.
A microscopic configuration-interaction (CI) methodology is introduced to enable bottom-up Schroedinger-equation emulation of unconventional superconductivity in ultracold optical traps. We illustrate the method by exploring the properties of Lithium-6 atoms in a single square plaquette in the hole-pairing regime, and by analyzing the entanglement (symmetry-preserving) and disentanglement physics (via symmetry-breaking, associated with the separation of charge and spin density waves) of two coupled plaquettes in the same regime. The single-occupancy RVB states contribute only partially to the …
We investigate the competition between antiferromagnetism and triplet superconductivity in quasi one-dimensional electron systems. We show that the two order parameters can be unified using a SO(4) symmetry and demonstrate the existence of such symmetry in one dimensional Luttinger liquids of interacting electrons. We argue that approximate SO(4) symmetry remains valid even when interchain hopping is strong enough to turn the system into a strongly anisotropic Fermi liquid. For unitary triplet superconductors SO(4) symmetry requires a first order transition between antiferromagnetic and superc…
