commit 459aa52d5e0aab5bc5074e5f343ba7af46bc9b53
parent cbb1537f28a49b20d17d09180288240049f72b39
Author: Miroslav Urbanek <mu@miroslavurbanek.com>
Date: Thu, 29 Jun 2017 02:51:46 +0200
Add a simulation of boson expansion
This calculation is similar to the calculation of many-body
localization. However, there is no random potential.
Diffstat:
| README | | | 21 | ++++++++++++++++++--- |
| examples/expans.lisp | | | 105 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| outputs/expans | | | 309 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
3 files changed, 432 insertions(+), 3 deletions(-)
diff --git a/README b/README
@@ -93,6 +93,12 @@ There are several examples in the directory "examples":
$ ./run inputs/mbl.lisp
$ ./run examples/mbl.lisp
+* Boson expansion in two dimensions ("expans.lisp").
+
+ This example is inspired by article [4]. Usage:
+
+ $ ./run examples/expans.lisp
+
The sample outputs are in the directory "outputs".
4. FILES
@@ -118,17 +124,26 @@ tebdol/tensor.lisp: Symmetric tensor routines.
tebdol/ttns.lisp: Routines for working with tree tensor network states.
tebdol/util.lisp: Miscellaneous utilities.
-5. REFERENCES
+5. AUTHOR
+
+Miroslav Urbanek <miroslav.urbanek@mff.cuni.cz>
+
+6. REFERENCES
[1] M. Urbanek and P. Soldán, "Parallel implementation of the
time-evolving block decimation algorithm for the Bose–Hubbard model",
Comput. Phys. Commun. 199, 170–177
(2016). doi:10.1016/j.cpc.2015.10.016
-[2] Trotzky S. et al., "Probing the relaxation towards equilibrium in
+[2] S. Trotzky et al., "Probing the relaxation towards equilibrium in
an isolated strongly correlated one-dimensional Bose gas", Nature
Physics 8, 325–330 (2012). doi:10.1038/nphys2232
-[3] Choi J.-y. et al., "Exploring the many-body localization
+[3] J.-y. Choi et al., "Exploring the many-body localization
transition in two dimension", Science 352, 1547–1552
(2016). doi:10.1126/science.aaf8834
+
+[4] J. Hauschild et al., "Sudden expansion and domain-wall melting of
+strongly interacting bosons in two-dimensional optical lattices and on
+multileg ladders", Physical Review A 92, 053629
+(2015). doi:10.1103/PhysRevA.92.053629
diff --git a/examples/expans.lisp b/examples/expans.lisp
@@ -0,0 +1,105 @@
+;; hard-core boson expansion in a two-dimensional optical lattice
+
+;; parameters
+
+(defparameter *width* 6)
+(defparameter *height* 6)
+(defparameter *diameter* 2)
+
+(defparameter *jy* 5d-1) ;; *jx* = 1
+
+(defparameter *step* (/ 16d0))
+
+(defparameter *maxdim*
+ (list (* (expt 2 32) double-float-epsilon) nil 128))
+
+;; libraries
+
+(load "conf.lisp")
+(require :tebdol)
+
+(use-package '(:blas :ttns :tebd :bhm))
+(setf *print-level* 2)
+
+;; functions
+
+(defun radius-x (pn n)
+ (loop
+ with w = (array-dimension pn 0)
+ with h = (array-dimension pn 1)
+ with c = (- (/ w 2) 5d-1)
+ for i below w
+ sum (* (expt (- i c) 2)
+ (loop
+ for j below h
+ sum (aref pn i j)))
+ into s
+ finally (return (sqrt (/ s n)))))
+
+(defun radius-y (pn n)
+ (loop
+ with w = (array-dimension pn 0)
+ with h = (array-dimension pn 1)
+ with c = (- (/ h 2) 5d-1)
+ for j below h
+ sum (* (expt (- j c) 2)
+ (loop
+ for i below w
+ sum (aref pn i j)))
+ into s
+ finally (return (sqrt (/ s n)))))
+
+(defun make-square-ttns (width height diameter dimension)
+ (loop
+ with p = (make-vacuum-ttns width height dimension)
+ with xshift = (ceiling (- width diameter) 2)
+ with yshift = (floor (- height diameter) 2)
+ for i below diameter
+ do
+ (loop
+ for j below diameter
+ do (ttns-create-particle p (+ i xshift) (+ j yshift) dimension))
+ finally
+ (compress-ttns p nil)
+ (return p)))
+
+;; main
+
+;; hard-core bosons
+(defparameter *dimension* 2)
+(defparameter *particles* (expt *diameter* 2))
+(defparameter *potential* (make-array (list *width* *height*) :initial-element 0d0))
+
+(defparameter *tbhsh* (bose-hubbard-site-hamiltonian *dimension* *jy* 0d0 0d0))
+(defparameter *ssps* (make-ssps *width* *height* *dimension* 0d0 *potential* (/ *step* 2)))
+(defparameter *dsps* (make-dsps *width* *height* *dimension* 0d0 *potential* (/ *step* 2)))
+(defparameter *dspy* (make-double-site-propagator *tbhsh* *tbhsh* (/ *step* 2)))
+
+(defparameter *ttns* (make-square-ttns *width* *height* *diameter* *dimension*))
+(defparameter *pn* (all-pn-operators *width* *height* *dimension*))
+
+(format t "# width = ~A~%" *width*)
+(format t "# height = ~A~%" *height*)
+(format t "# diameter = ~A~%" *diameter*)
+(format t "# jy = ~A~%" *jy*)
+(format t "# step = ~A~%" *step*)
+(format t "# maxdim = ~A~%" *maxdim*)
+(format t "~%# time radius-y radius-y imbalance norm~%# ----~%# density~%# ----~%~%")
+
+(loop
+ for i to 32
+ do
+ (unless (zerop i)
+ (ttns-tebd-evolve *ttns* *ssps* *dsps* *dspy* *maxdim*))
+ (let* ((n (realpart (ttns-overlap *ttns* *ttns*)))
+ (p (all-pn *ttns* n *pn*)))
+ (format
+ t
+ "~,4F ~F ~F ~F~%"
+ (* i *step*)
+ (radius-x p *particles*)
+ (radius-y p *particles*)
+ n)
+ (format t "----~%")
+ (print-pn p)
+ (format t "----~%")))
diff --git a/outputs/expans b/outputs/expans
@@ -0,0 +1,309 @@
+# width = 6
+# height = 6
+# diameter = 2
+# jy = 0.5d0
+# step = 0.0625d0
+# maxdim = (4.768371582031251d-7 NIL 128)
+
+# time radius-y radius-y imbalance norm
+# ----
+# density
+# ----
+
+0.0000 0.5 0.5 1.0
+----
+0.0 0.0 0.0 0.0 0.0 0.0
+0.0 0.0 0.0 0.0 0.0 0.0
+0.0 0.0 1.0 1.0 0.0 0.0
+0.0 0.0 1.0 1.0 0.0 0.0
+0.0 0.0 0.0 0.0 0.0 0.0
+0.0 0.0 0.0 0.0 0.0 0.0
+----
+0.0625 0.5077566797893776 0.5019441928156417 0.9999957100380382
+----
+0.0 0.0 0.0 0.0 0.0 0.0
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+----
+0.1250 0.5303148492900793 0.5077108829878988 0.99999135288408
+----
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+----
+0.1875 0.565826537560451 0.5170994116788645 0.9999872019591837
+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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+----
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