arXiv (Cornell University),
Journal Year:
2023,
Volume and Issue:
unknown
Published: Jan. 1, 2023
We
discuss
a
tensor
network
method
for
constructing
the
adiabatic
gauge
potential
--
generator
of
transformations
as
matrix
product
operator,
which
allows
us
to
adiabatically
transport
states.
Adiabatic
evolution
networks
offers
wide
range
applications,
two
are
explored
in
this
paper:
improving
optimization
and
scanning
phase
diagrams.
By
efficiently
transporting
eigenstates
quantum
criticality
performing
intermediary
density
renormalization
group
(DMRG)
optimizations
along
way,
we
demonstrate
that
can
compute
ground
low-lying
excited
states
faster
more
reliably
than
standard
DMRG
at
or
near
criticality.
simple
automated
step
size
adjustment
detection
critical
point
based
on
norm
potential.
Remarkably,
able
through
models
study.
The
minimally
entangled
typical
thermal
states
(METTS)
are
an
ensemble
of
pure
states,
equivalent
to
the
Gibbs
state,
designed
with
efficient
tensor
network
representation
in
mind.
In
this
article,
we
use
projected
pair
(PEPS)
as
their
on
a
two-dimensional
(2D)
lattice.
Unlike
matrix
product
(MPS),
which
for
2D
systems
limited
by
exponential
computational
barrier
lattice
size,
PEPS
provides
more
tractable
approach.
To
substantiate
prowess
modeling
METTS
(dubbed
PEPS-METTS),
benchmark
it
against
purification
method
context
quantum
Ising
model
at
its
critical
temperature.
Our
analysis
reveals
that
PEPS-METTS
achieves
accurate
results
significantly
lower
bond
dimensions.
We
further
corroborate
finding
Fermi-Hubbard
model.
At
technical
level,
introduce
zipper
obtain
boundary
MPS
needed
compute
expectation
values
and
perform
sampling.
imaginary
time
evolution
is
done
neighborhood
update.
Physical Review Letters,
Journal Year:
2024,
Volume and Issue:
133(25)
Published: Dec. 19, 2024
Recently,
robust
d-wave
superconductive
(SC)
order
has
been
unveiled
in
the
ground
state
of
2D
t-t^{'}-J
model-with
both
nearest-neighbor
(t)
and
next-nearest-neighbor
(t^{'})
hoppings-by
density
matrix
renormalization
group
studies.
However,
there
is
currently
a
debate
on
whether
SC
holds
up
strong
t^{'}/t>0
t^{'}/t<0
cases
for
model,
which
correspond
to
electron-
hole-doped
sides
cuprate
phase
diagram,
respectively.
Here,
we
exploit
state-of-the-art
thermal
tensor
network
approach
accurately
obtain
diagram
model
cylinders
with
widths
W=6
down
low
temperature
as
T/J≃0.06,
pushing
boundaries
contemporary
finite-T
calculations.
For
t^{'}/t>0,
find
domelike
regime
diverging
pairing
susceptibility,
χ_{SC}∝1/T^{α}
below
characteristic
T_{c}^{*}.
Near
optimal
doping,
T_{c}^{*}
reaches
its
highest
value
about
0.15J.
Above
yet
higher
crossover
T^{*},
magnetic
susceptibility
becomes
suppressed,
can
be
related
onset
pseudogap
(PG)
behaviors.
On
other
hand,
t^{'}/t<0,
correlations
are
much
weaker,
although
exhibits
node-antinode
structure
PG
observed
cuprates.
The
calculations
underscore
similarities
differences
finite-temperature
between
fundamental
cuprates,
yielding
unique
insights
into
their
intricate
Physical Review Letters,
Journal Year:
2025,
Volume and Issue:
134(11)
Published: March 18, 2025
The
two-dimensional
Hubbard
model
is
widely
believed
to
capture
key
ingredients
of
high-Tc
superconductivity
in
cuprate
materials.
However,
compelling
evidence
remains
elusive.
In
particular,
various
magnetic
orders
may
emerge
as
strong
competitors
superconducting
orders.
Here,
we
study
the
ground
state
properties
doped
t−t′
on
a
square
lattice
via
infinite
projected
entangled-pair
method
with
U(1)
or
SU(2)
spin
symmetry.
former
compatible
antiferromagnetic
orders,
while
latter
forbids
them.
Therefore,
obtain
by
comparison
detailed
understanding
impact
superconductivity.
Moreover,
an
additional
t′
term
accommodates
particle-hole
asymmetry,
which
facilitates
studies
discrepancies
between
electron-
and
hole-doped
systems.
We
demonstrate
that
(i)
positive
t′/t
significantly
amplifies
strength
orders;
(ii)
at
sufficiently
large
doping
levels,
t−t′
favors
uniform
instead
stripe
states
charge
modulations;
(iii)
enhancement
frustration,
increasing
either
next-nearest
neighbor
interactions
doping,
impairs
helps
stabilize
Published
American
Physical
Society
2025
PRX Quantum,
Journal Year:
2024,
Volume and Issue:
5(2)
Published: June 14, 2024
We
discuss
a
tensor
network
method
for
constructing
the
adiabatic
gauge
potential—the
generator
of
transformations—as
matrix
product
operator,
which
allows
us
to
adiabatically
transport
states.
Adiabatic
evolution
networks
offers
wide
range
applications,
two
are
explored
in
this
paper:
improving
optimization
and
scanning
phase
diagrams.
By
efficiently
transporting
eigenstates
quantum
criticality
performing
intermediary
density-matrix
renormalization
group
(DMRG)
optimizations
along
way,
we
demonstrate
that
can
compute
ground
low-lying
excited
states
faster
more
reliably
than
standard
DMRG
at
or
near
criticality.
simple
automated
step
size
adjustment
detection
critical
point
based
on
norm
potential.
Remarkably,
able
through
models
study.
Published
by
American
Physical
Society
2024
Nature Communications,
Journal Year:
2024,
Volume and Issue:
15(1)
Published: Aug. 15, 2024
Traditional
magnetic
sub-Kelvin
cooling
relies
on
the
nearly
free
local
moments
in
hydrate
paramagnetic
salts,
whose
utility
is
hampered
by
dilute
ions
and
low
thermal
conductivity.
Here
we
propose
to
use
instead
fractional
excitations
inherent
quantum
spin
liquids
(QSLs)
as
an
alternative,
which
are
sensitive
external
fields
can
induce
a
very
distinctive
magnetocaloric
effect.
With
state-of-the-art
tensor-network
approach,
compute
low-temperature
properties
of
Kitaev
honeycomb
model.
For
ferromagnetic
case,
strong
demagnetization
effect
observed
due
Z2
vortices
via
fractionalization,
described
equation
state
with
renormalized
Curie
constant.
antiferromagnetic
uncover
intermediate-field
gapless
QSL
phase
large
entropy,
possibly
emergence
spinon
Fermi
surface
gauge
field.
Potential
realization
topological
excitation
magnetocalorics
materials
also
discussed,
may
offer
promising
pathway
circumvent
existing
limitations
hydrates.
Recently,
frustrated
magnets
have
attracted
interest
for
applications.
Here,
using
numerical
calculations,
authors
find
pronounced
magnets,
ascribed
fractionalized
liquid
regime.
arXiv (Cornell University),
Journal Year:
2023,
Volume and Issue:
unknown
Published: Jan. 1, 2023
The
newly
discovered
high-$T_c$
nickelate
superconductor
La$_3$Ni$_2$O$_7$
has
generated
significant
research
interest.
To
uncover
the
pairing
mechanism,
it
is
essential
to
investigate
intriguing
interplay
between
two
$e_g$,
i.e.,
$d_{x^2-y^2}$
and
$d_{z^2}$
orbitals.
Here
we
perform
an
infinite
projected
entangled-pair
state
(iPEPS)
study
of
bilayer
$t$-$J$
model,
directly
in
thermodynamic
limit
with
orbitally
selective
parameters
for
orbitals,
respectively.
electrons
exhibit
intralayer
hopping
$t_\parallel$
spin
couplings
$J_\parallel$,
interlayer
$J_\perp$
passed
from
electrons.
However,
$t_\perp$
negligible
this
case.
In
contrast,
orbital
demonstrates
strong
$J_\perp$,
while
inherent
$J_\parallel$
are
small.
Based
on
iPEPS
results,
find
clear
orbital-selective
behaviors
La$_3$Ni$_2$O$_7$.
orbitals
robust
superconductive
(SC)
order
driven
by
coupling
$J_\perp$;
band
shows
relatively
weak
SC
as
a
result
small
(lack
coherence)
but
large
(strong
Pauli
blocking).
Furthermore,
substituting
rare-earth
element
Pm
or
Sm
La,
enhanced
order,
which
opens
up
promising
avenue
discovering
superconductors
even
higher
$T_c$.
Quadratic
band
touching
(QBT)
points
are
widely
observed
in
two-
and
three-dimensional
(2D
3D)
materials,
including
bilayer
graphene
Luttinger
semimetals,
attract
significant
attention
from
theory
to
experiment.
However,
even
its
simplest
form,
the
2D
checkerboard
lattice
QBT
model,
phase
diagram
characterized
by
temperature
interaction
strength,
still
remains
unknown
beyond
weak-coupling
regime.
Intense
debates
persist
regarding
existence
of
various
interaction-driven
insulating
states
this
system.
To
address
these
uncertainties,
we
employ
thermal
tensor
network
simulations,
specifically
exponential
renormalization
group
tangent
space
group,
along
with
density
matrix
calculations
provide
a
comprehensive
finite-temperature
for
model
shed
light
on
previous
ambiguities.
Notably,
our
findings
reveal
emergence
robust
bond-nematic
Dirac
semimetal
distinct
thermodynamic
properties
that
set
it
part
nematic
state
other
symmetry-broken
states.
This
previously
overlooked
feature
is
found
be
ubiquitous
interacting
systems.
We
also
discuss
implications
results
experimental
systems
such
as
iridate
compounds.
For
quantum
many-body
systems
in
one
dimension,
computational
complexity
theory
reveals
that
the
evaluation
of
ground-state
energy
remains
elusive
on
computers,
contrasting
existence
a
classical
algorithm
for
temperatures
higher
than
inverse
logarithm
system
size.
This
highlights
qualitative
difference
between
low-
and
high-temperature
states
terms
complexity.
Here,
we
describe
finite-temperature
using
matrix
product
state
formalism.
Within
framework
random
samplings,
derive
an
analytical
formula
required
number
samples
which
provides
both
quantitative
measures
At
high
low
temperatures,
its
scaling
behavior
with
size
is
linear
quadratic,
respectively,
demonstrating
distinct
crossover
these
numerically
difficult
regimes
difference.
